I've been struggling vs Falcon as Fox recently too. I can't beat my local Falcon player at all lmao!!!
The advice Jtails gave me vs Falcon is to pay attention to what he is doing at neutral. Falcon is linear more or less, his main options being dash grab and spacing moves like bair and maybe a dash attack every now and again? You can kind of use that to dictate how you move at neutral, doing your best to avoid grab and bair specifically.
At low %'s the Utilt string doesn't work like vs the other fast fallers. I tend to do Utilt -> grab because people tend to block and look for a block punish. I believe he can mash jab out of that though, so utilt -> block -> grab might be better. Utilt strings I start going for at around 20%, and the combo game on Falcon is very strong.
The strongest thing in this match up that you absolutely need to do is hit him out of his up b. If you can time D-Smash to hit his hands on the way up he more or less will die for it, and if you can time u-tilt -> bair he will more or less die for that too. It's super important to do this, because Fox typically wont risk going off stage to gimp Falcon and that's kinda a big deal vs a character who is "bad" because he's easy to edge guard.
Anyways good luck, I'm still trying to figure this match up out too so I don't have much more to contribute v-v