Neutral boyz
In neutral peach is a zoning character. If you observe where you are on the stage compared to her you can imagine the different spaces she is actively attempting to be in, and so predict what she wants to do:
Is she doing a lot of dashing away and retreating ariels? That means she wants to get enough space to pull a turnip.
If she is a bit closer than that, as in she is trying to be in and out of turnip pull/your face, then she is baiting you to rush her to stop the turnip pull so she can hit you with an unreactable dash attack.
Often times versus peach you want to open the game with a neutral start, or rather if you are like me and think that's lame and boring then just quickly give yourself space to shoot some lasers and test their powershielding prowess. It's important because How well they control the ground game when fighting you is based a lot on how well they deal with lasers. If they can powershield well, expect the first two zones I mentioned, turnip pulling and dash attack zones, to be way more potent. Fortunately most peaches aren't amazing at powershielding, but if they are then you are gonna have a much harder time.
So lets go over a bit more under the assumption that your laser game is better than them dealing with lasers, i.e. they don't armada turnip toss you after a powershield into downsmash. If they can't handle lasers too well they want to enter one of the other 3 zones peaches tend to use:
Above laser height. This is by far the most popular thing peaches do versus falco. It's easy, it's threatening to you, it steals your best tools. They essentially can deploy platform camping from center stage with decent drift and float canceled ariels. If you want to fight a peach, you are going to have to know how to deal with this space. First let's just say it isn't a great idea to uptilt like FE_Hector said. The reason is that it simply isn't worth the risk reward. Think of it this way: if they are above you in a position that lasers, ariels, and waveshine can't effectively hit, what advantages are in the uptilt? It is an awkward hitbox to start up, as you have to approach under her in a dangerous spot, facing backwards (AC bairs are terrible against peach, too), and she is literally just waiting for you to try and use one of your options to overextend already. Even if you do manage to read the exact time she will FC ariel you, she will almost always trade with you. If it's her fair against your one up tilt, she will ride that trade to the bank, and that's being generous. Sometimes she will just read the time of your option and straight up beat your move. So how do you beat it?
The key is to mix up your timings and treat her like she is sort of platform camping. Peach can beat a lot of your options by drifting in the above-lasers-zone, and she will get a ton of mileage on you if you play in cadence. Most falco's will use an option, then immediately another, then immediately another, leaving hella start up between moves or just straight up giving away hits. If she knows you are going to take action at a specific time, it doesn't matter that you have a great tool kit for her to be intercepted, she'll just time all her FC ariels so that they cover more than one thing. Think of it like how you if you are a falco and a sheik is in shield, and you don't know what the sheik will do, but you do know when she'll act oos. You can cover shield grab, spot dodge, and defensive f-tilt all by delaying your approach with a tiny dash dance away and back in, because they all last around the same time with around the same punish window. This is how peaches will treat you if you spam a predictable approach. you just spam lasers one after another, you are going to eat a meaty fair to the face, if you shoot a laser then immediately do an approach option, she can read that obvious move and delay the right amount to cover most stuff then fair you there. The great news is that as long as you aren't predictable you have an advantage. Peach can only float for a max of around 2.5 seconds, and you can see when she is about to lose her float by observing the starts glittering off of her (they start to vanish and dim when she is within the last half second or so). You could also just keep mental track. Either way the advantage is simple: If she doesn't act with a float canceled ariel before this then she will have a laggy ariel or will have to do a slow as heck double jump you can wreck with so many options. THIS is the meat of dealing with this zone. If she falls down to try and ariel early, try to be patient and snipe her. Predict the time that she will start to fall and poke her with a fairly close laser, one that keeps you pretty safe and able to dash back if it misses. Be deliberate about it, make each time you choose to laser a read, so she can't just smack you for doing one after another. If you land the laser he options from there SUCK. Her fair is too slow, her nair is small, her momentum is stopped so you can beat everything she wants to do except double jump but that is also bad. Not to mention every ariel she tried to fall with after you sniper her is laggy. This situation right here is what you want to excel in, and it is what wins falco the match up. If she can't handle the lasers on the ground she takes to the sky and you kill her float canceled ariel without risking much and then punish right after. You can do more than just laser her there, really, all your options timed perfectly will work, but I'm pretty sure a higher laser is the best. You risk almost nothing and she can't beat the hitbox, along with momentum stopping.
finally next zone lol
Side platform. Normally I consider the last two zones, top plat and side plat, the same zone because most charactyers can get to each quickly. But in peach's case she cannot with her slow DJ, so I'll quickly look at both. For the side platform I recommend treating is like a float with more start up on FC ariels and a downsmash. Peach players that aren't MacDizzle (the king btw) or aren't on FoD will often avoid this zone. It doesn't hold much potential outside of you jumping into to a silly downsmash and they can't do much on the plat but dash dance and run off. She falls so slow the laser on her is free sometimes. But be a little careful, if she falls through the platform and you laser her she will keep her float, something you wouldn't worry about after snuffing a FC move in the above-laser-height zone. Other than that, have at her. Again, don't get downsmashed. It's like getting hit with all of the FeelsBadMan memes at once. ;-;
Top platform. Oh yes the top platform. this is the kind of thing I expect to see from old armada before he became god tier at ground play. Go watch really old PPMD vs Armada games from like 2010, Professor Urine PHD pressures armada out of every zone but this one very often. I honestly know the least about dealing with this one, since a majority of peaches are reluctant to go up there for some reason. The bad news for you, the falco, is that your options mostly suck to punish her. She can see every move coming and react way easier than the above-laser-height zone, and can nair the crap out of you. And when you do land a hit it is usually stray. The key here is to not worry too much about comboing and land some full hop double lasers or bairs to knock her out of that comfort zone. You have to be a little patient here, most falco's will see this as an opportunity to go in hard and get poooped on. Just get some free damage and work in some interesting punishes now and then when you are used to this zoning. I like to try and stay below middle platform until they get uncomfortable and move to the left or right a bit so I can FH double laser and land on top platform, but not all peaches will make that easy. They can float at what is essentially just above those laser heights and treat a dumb approach the same way they do near the ground. Double jumping is super risky to reach them up close so if you are gonna do that and get free lasers make sure you don't get hit.
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Waaaay easier to follow punishes:
I totally agree with the idea that less is more with falco v. peach. Yoshi's can let you kill off the top sometimes, and in general you are not going to get too many early kills.
Low%: Land stray hits with your better options in neutral. If you land a strong low dair you can link shine to DJ FF dair through and then shine on platforms. Overall you land some grabs on them and steal stage control/get some simple stuff. Honestly if you want to know how to combo peach just watch PP. I know I've been citing him a lot but if there is anybody that wrote the book here it's him, and you can see how he follows up on certain things.
Like was said earlier you never want to laser her after her up-b. Generally you want to land a good back air. There are a ton of little mix-ups she can do and you almost never get a kill easy on peach. Really this is why people think she wins the match up when she doesn't. She lives forever on most maps and you die super fast sometimes. Just try to bair with it (im sorry) and be stronger in the head than the peach. Be patient. Remember that while she does gain some moral when she survives with great DI, she can only get smacked around in neutral so much before no amount of good DI can save her stock, OR her mental state. It's honestly frustrating to feel like you are putting in a ton of work, but it is just as frustrating to get tossed around like the sandbag for a minute and a half off stage.
If anything else for edge guarding I'd say play around with your side-platform movement to make it hard to predict how you'll approach. And if you get them on ledge try to punish all their options. I love the Crap PP does where he walks up to ledge as their invincibility frames end and threatens with a low tilt like f-tilt or down-tilt. If they immediately input an option he retreats back a bit to cover roll and jump from ledge. If they don't he can possibly kill them with a tilt.
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Your defense options
While it feels like you just get tossed around and walled out after a mistake you still have options. Peaches do series of edge guards now that Armada videos taught them where it seems like they cover everything. But really they require some tight timing windows and fast decision making after they land first hit, and first hit is often a mix-up. They usually cover instant side-b or high firefox, but it's pretty hard to cover both so they pick one. You can shine stall, but peach really just wants you to do that since she's slow and want to get near the ledge asap after that first hit. Watch a ton of armada edge guards then compare them to each other, what did he do the times that he missed? Did he do that identical thing somewhere else but it hit, and what was he trying to cover? Really avoiding the peach edge guard comes down to a hard read on what they are trying to cover the most, and acting accordingly to avoid just that. Sure, this method is bad for pure option coverage, but they are going to cover your best options more often.
Crouch cancel
Crouch cancel is NOT TERRIBLE vs. peach. It is sometimes, the same way spamming shine after each ariel you use can get you rekt. You really only want to use this when you think they want to dash attack you. If they are doing other stuff it's pretty bad, especially FC ariels.
SDI
A lot of peaches now like to Dair you as a combo starter. I really don't know why and it shouldn't work on you with enough practice. If you are recovering you want to SDI in a 12 to 9 o'clock quarter circle back and forth fast af boyyy when they try to dair you. If you do this and finish with upward DI you can survive a nair that sends you the wrong way. Peaches can delay and only hit you with the last few hits if you are trying to up b, but you can mix them up by riding the wall sometimes so that they have a 50/50 where they either give you time to SDI or miss the hit and give you ledge.
When on the ledge you can try to instant DJ side B if they float over you, as they have a hard time chasing your momentum. Just don't do this if they are grounded. If they are far away in center stage to a ledge hop double laser. There is no harm in trying your hardest to master ledge dashing, either, it is super useful.
Shine Bright like a diamond, except don't do it in dumb ways. Most falco's just cover themselves with shines like it is universally better than other options, when really they just add a couple frames of lag to let the opponent downsmash them if they do it every time. I forgive you if you do it, though. Falco's were born to shine.
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AYYY LMAO
This is a long post haha.
Either was fun to write. I like to organize my thoughts like this. I love peach as a MU because she is one of the only characters who actively try to macro-space and zone; they usually have game plans and strategies to use one after another. It's more like chess or something like that than just a ton of neutral exchanges. Nice for a change imo.
Hope it helps and ask if you need help with anything specific!
(also, if you know anything about the Fox/Peach matchup, I need help on that one too. My secondary is Fox) Thanks in advance 
Audos
. For the record, I'm not talking about when she's clearly above all of your options, but instead when she's at that extremely annoying height where even the highest laser just barely misses her. In that case, the utilt will work, and shine turnaround AC bair is a very quick input that they'd have to read to space around if you're mixing yourself up properly.