"Ok so the information here is a little outdated. *Looks at '04 posts*
CF has some BS he can do to peach. A grab at 0 means a dthrow chain till about 20 (assuming you DI away), then an uthrow into a couple of uairs (across the stage). All in all about 60%. Assuming you DI towards on the uthrow, you then eat a nair combo which does who knows how much % and goes for until the stage runs out.
Basically if CF grabs you, you're pretty lucky to get out before 60%. Considering peach dies at 120 latest from the knee, that's half your stock from one grab.
Above that, nair/uair combos get easier which almost always end in knee, and peach (and everyone else) die really fast from that move. However Peach is probably 2nd best at surviving the knee-after samus.
------------------
However, peach can combo CF back. Tilts, uairs, and dash attacks into fairs are great and a lot of fun. Dsmash is a great weapon (as usual), and does a great job beating a lot of his approaches. If you do CG, you can start around 30-35ish and go till about 80.
As counters, dash attack, downsmash, umbrella, and fsmash (too a lesser extent usmash and ftilt) are all spectacular for beating his approaches. Utilt might work too, but I haven't tried it.
Jumping gets you owned in this match, because he can pretty easily intercept you out of the air with a nair, then grab you-> 60% to you.
Generally DIing away from dthrow allows you to get a nair in before/while getting kneed at higher percents. if you're gonna die, might as well do it with a trade. DIing away from combos is typically the best to do as well (because you get to the other side of the stage faster), until you get right to the edge. Sometimes changing your DI from away into up and towards when hit by the last uair can save you from a knee. Don't get caught DIing away when he goes for the knee.
Smash DIing and Cstick DIing (down/away/towards--i think it's down) can get you out of nair combos, from what I understand. Definitely good to try/learn.
------------------
Overall this matchup is very even, where Peach used to own CF, it's now (IMO) one of the most even matchups in the game. Both characters get to own each other a lot."