Peach is pretty underrated, and can give falco trouble if you don't know what you're doing.
Firstly, Peach cannot be chaingrabbed, so dthrow follow-ups are going to be very essential in this match-up. Peach, on the other hand, DOES have a chaingrab on falco. 30% + ftilt. So be mindful of that.
Turnips. Falco shouldn't really have too much trouble with these, since he has the reflector and there's always the option of shielding. Watch out for Granny Turnips though, since they really hurt (even though they have a really low chance of coming out). Just because Peach is holding a Turnip, don't just mindlessly throw your reflector out because you'll just be punished. Be patient and space yourself out of range from the turnip with lasers, and shield if she gets really close and throws it. Only reflector when you're a decent distance away.
Peach enjoys following up turnips with floating aerials, especially dair for shield pressure. If she starts floating above you, shield the aerial and then immediately retaliate with SH Nair or bair OoS. Be sure to follow her DI because they're more than likely to float away after the aerial is finished, and use the appropriate aerial for wherever she is (behind, bair. Above or in front, nair).
Peach is very capable of gimping falco's phantasm, so be sure to sweetspot if you know they're not going to edgehog. It is possible to dair her out of the parasol, but it's probably just best to edgeguard with bairs and get as much damage as possible.
Falco has an easier time racking up damage, even without the chaingrab thanks to dthrow follow-ups, jabs, lasers, IAP's and aerials. In order for Peach to keep up, she needs to get in quite close to really pack a punch. But when she DOES get in, falco is in a world of pain.
Falco's best killing option is usmash. Peach would probably go for gimps with nair or something on phantasm. She also has the almighty fair at her disposal, and utilt can kill surprisingly well. You do not want to be above peach anyway since she can outrange dair.
It's probably not a wise idea to pick japes against Peach. She actually does really well there, and we have no 0-death. I don't think it's banworthy though.
Falco would want to play on FD, BF and possibly Rainbow Cruise. Peach sucks at that stage. I'd say the best bet though would be BF since it's hard for her to float above falco for dairs and whatnot (still possible), while the platforms give peach a hard time approaching.
In the past I've been CP'ed Luigi's Mansion and Delfino. I'd probably ban Luigi's but that's just me. Peach can really screw you over on Delfino, since the stage works quite nicely for her. Oh, and whatever you do, DO NOT play on Lylat for the first match of a tourney set. It's probably her best neutral (if it's neutral at your tournies).
Overall, I'd say 50:50, or possibly 55:45 falco's favour for this match-up. Falco has good damage racking and can space well, while peach has gimps, aerial priority, good edgeguarding and a chaingrab at her disposal.
