Against Falcon, focus your game around staying grounded and non committal. He punishes us really hard in general, but specifically for being aggressive (unless we've got him in a techchase or something), Falcons like defaulting to spaced nair against us, because it deals with her basic float heights pretty well, so you want to:
1. Stay grounded when you're not that close to him but STAY MOBILE on the ground. Lots of WD back, dash dancing. You don't have the large DD that he has, but Peach's moves are generally larger, and a lot faster (I'm speaking of nair/bair here). You're staying mobile in order to avoid grabs and change how Falcon can approach you (the closer you are, the more likely it is that you can threaten him with dash attack, and so he has to respect this (he'll be more wiling to throw out shields/jumps to evade potential dash attacks). The further away you are, the more he needs to worry about you pulling a turnip or setting up a float that he can't punish). He'll generally resort to DD'ing while closing space, scouting for a bad turnip pull or a bad float.
2. Look for moments when you can either shield the nair for a punish, CC it for a punish, or a dash attack it (rather risky vs him) for a punish. You'll more often than not need to WD back to get the punish on his nair, because of how far his jump sends him. WD back into downsmash, shield, dtilt, dash attack are all decent punishes. SDI up + away on his nair is good as well.
Against Falcon, keep the amount of laggy moves (hopeful dsmashes, hopeful dash attacks, hopeful FJ nairs) that you throw out to a bare minimum. You can use some low FC bairs to force him to respect you in neutral, but only when you've gotten close to him, so he can't threaten you with the full length of his dash jump. Avoid jumping when there's a decent amount of space between you two (his dash jump length gives him much more leeway to interact with you than vice versa), but when you're close, you can use low float aerials to pressure him/keep him locked down. Our aerials start faster than his, so when you're close, you can catch his jumps with nair/bair, as well as just exert overall pressure over Falcon. Especially if you suspect a dair from him, nairing his jump/startup of dair is a decent strategy vs him.
Fair is still good in this matchup, as it is in all matchups, but be very guarded with how you set up for it. It is very vulnerable to being beaten by nair/uair. I recommend saving it for when you're close enough to threaten Falcon and keep him from wanting to jump (or when he's in shield).
Working a good pressure mixup game when close (FC bairs/nairs into grab/dsmash), mixed with a good, conservative game when you're further away from him (Using your short but potent mobility to scout out approaches/feign openings and punish Falcon with WD/DD) will help you in this matchup. Keep your turnip pulls restricted to edgeguards or moments when Falcon is FAR away from you, otherwise they are easy for him to punish. Once you have one out, you can influence how he has to move on stage, but remember that you have turnips to poke/probe/inhibit your opponent's movement, NOT just as a means for approach.
Make sure you know your CG (1-77%, so basicaly 1-80%. And the "1" is important because the CG does not work from 0.) Know how to convert off of dash attack from mid 30s (grab, FC uair, SH uair, nair will be your main conversions). Also know how to convert off of dtilt (similar percents as for dash attack, though dtilt gives you more leeway with its higher stun). End your combos with him offstage, and edgeguard him from there.
Edgeguarding Falcon is fairly straightforward. If he's going low, you can usually float dair at the ledge and catch his sweetspot attempt. If you know he's going for a sweetspot and you have the time, WD FF to the ledge is extremely good and worth learning for every Peach. The goal is to put your aerials between him and the stage until he dies. If you get the opportunity to combo him back offstage (with a weak nair > strong nair, bair > bair, etc), then go for it. If you know the Falcon is going to go high, you can pull a turnip and try to control him that way, but high is generally the most difficult for Peach to cover. Try to hit him offstage as low as you can.
Defensive DI: Not much here to write. DI down + away on uairs most of the time (be careful if he's leading you offstage, down+away on an errant uair could kill you).
I've seen DoH (I think it was him?) DI uairs up and in, and that makes it tricky for Falcon to follow up, sometimes. Just don't DI straight up expecting knee, that only makes knee easier to hit.
Mix your DI up between down+away and up+in on dthrow. It will make the conversion harder for him if he has to react to your DI (rather than him just autopilot kneeing you). Look for points where you can DJ + airdodge out of the dthrow (normally on down+away DI, typically the hardest for him to hit).
Hopefully this helps, and isn't too confusing. My knowledge on Fox is sparse and ever changing, so I won't try to give too much on that front. Just watch Armada videos and try to look for how he gets his solid hits on Fox (it helps knowing how Foxes tend to deal with Peach's attempts to close the distance, assuming they're campy Foxes).