Dash attack combos falcon good... but you gotta be careful, cause one jump/dd means you'll miss him totally and he's free to punish you with whatever he desires, from grabs to aerials... and never forget that a grab from falcon is deadly, so shielding a dash attack is like free ko for falcon.
Dash attack works well as a chase though, falcon being a fast faller and heavy thing you can combo him into grabs and uairs and whatever you want. Funnily enough, well timed uair beats both his nair and dair approach. Uairs especially combo falcon very well, especially on platform stages.
Bair imo, can get through falcon's aerial attacks better than nair does. I rather not always be facing backwards against falcon though, so I often use nairs in a way that I float on or above the height falcon's usually short hop and nair, resulting in me getting the attack in there faster if I predicted his aerial approach or in some cases, even outprioritising him. Rising nair works well for this stuff too. Fair is good in a way of spacing, but falcon can just space much better and with much speedier aerial that his nair is, using fair too often as spacing method leads you to eat nair in the face with his long legs.
Nair-happy falcon can be punished with crouch canceling into nasty things, but knee and dair happy ones are more trickier cause of the stun to the shield and inability to cc them. Best bet is probably either avoiding them or shielding and then doing timely OoS stuff, especially if they mess that dair up and hit your shield too early. Float cancels/wd work on occasion if they like to do an aerial and then go dance around out of your OoS nair range for example, but you gotta predict the falcon if you wanna punish out of shield. They have many many options and spacing + running away usually leaves peach with little options to punish him.
I don't recommend too much turnip usage when on stage, but off stage one turnip can mean dead falcon. On stage, falcons can just kick you with nairs if you try a turnip approach and the turnip would just bounce from him, then his approaching speed is so fast you'll find yourself unable to even pull turnips safely, especially on smaller stages like yoshi. But if you get a turnip, a tricky approach often works the best and if you get a short hopped fc fair to something+dsmash, it'll likely go through his shield. Falcon doesn't like dsmash close to his shield as his legs become very vulnerable when his shield diminishes, but be extra careful about using dsmash when also spacing a lot. One dsmash not dealing stun to him means a knee/dair/combo to the face if the falcon is any competent in dealing with peaches.
When recovering back, watch out his uair. Prefer to get back from as high as possible so he can't reach you, then avoid that uair. You can be tricky and fast fall with bair to protect you for example, or dair when you think you've caught him off guard. But in any case, while uair is not superdeadly, it beats all your aerials so watch out for that one (not forgetting it can semispike on the ledge). If you need to sweetspot, be ready to meteor cancel and ledgetech those dairs if you can and be wary of falcon jumping at you off stage.
Cause falcon is so tricky, quick and dash dance happy, you as a peach must be as tricky and fast in your defense as well. Abuse your dd, shield and OoS options and even that wavedash. One wavedash might be just enough to keep falcon's spaced feet from hitting you and providing you with an opening. Crouch cancel punish immediately if you see an opening in his nairing. If you get him off stage, don't mess up this opportunity to edgeguard him. His recovery is very predictable, so you can even go all fancy at him and he'll never make it back in one piece.
If you want some vids of armada vs calle w's falcon, you should head to minisparken's tube account and see some (there's even a video where he 3 stocks armada's peach on a friendly D: ). Then there are some armada vs Dev's falcon on my own account Samochan, from around 4 months ago (armada 4 stocks him on dk64, poor dev).
I hope this helps, even a bit. <_>