O gawd... Falco... Out of my 3 worst MUs (MK, Falco, and Snake), I know the Falco MU the least...
Honestly, 90% of my experience is from playing against wifi falcos, which doesn't give me that much credibility in this matchup. Plus, I honestly have no clue what to do, so I just made up a style that fits me. I've been criticized by this style, but I've beaten a ton of Falcos on wifi with it (including Antis falco)
This works best at places like BF, the ship part of RC, SV, etc with a generally flat surface but a high platform. Get on the platform, double jump, hold the float, dair 3 times, get back on platform, repeat. It sounds really stupid, but there isn't much Falco can do. Sure, he can get on the platform and try to out-aerial you with like uair, bair, or nair, but I'm sure either Peach's dair will go through it, or you can maneuver around it and get in a bair. Falco can also try to laser you at that height, where you can just drop down really quickly, and try to punish his landing with whatever you want. I just kinda repeat this until Falco has high percent, then go for bairs/nairs/fairs for the final damage/kill. It's simple, but it kinda works.
My best neutral is probably BF and SV for the high platform. Then YI and PS1 because I like those stages in general, even though they're kinda bad for the matchup. And FD is my worst neutral (obviously) against Falco. I usually ban FD and get CP'd to Japes, which can work, but if Falco gets the lead, then this becomes 10x harder. And I CP Falcos to either Brinstar or Rainbow Cruise depending on what they ban, how campy they are, and how badly I wanna time them out lol
FC Nair works wonders against Falco. Just watch out for laser->anything (smashes, grabs, whatever). Turnips are never bad, but with lasers coming your way all the time, they're hard to pull out constantly. Plus Falco's reflector can be a pain.
Overall, I think it's 40:60. Falco definitely beats Peach unless someone develops some super combo or something, but I use my not-afraid-to-time-you-out style and just kinda wait Falco out =/ And no, I've never timed a Falco out, but I've gotten close