Crossup nair on their shield into instant (shine maybe) sh bair. This is really annoying for falcon to deal with as they can't really stomp OoS it or grab it. They'll have to roll and then you can start reacting to that.
If you can land a falling upair it's always really good. It's safe to crossup their sheild with a falling upair.
CCing falcon's aerials at low percent into dash jc grab.
Avoid
Spamming uptilt. They'll grab or knee you, and they'll probably DI it anyway. Uptilt is a good combo extender, but quite bad in neutral imo. Use sparingly. Try spamming sh bair inplace instead.
Going for too many grabs at low percent. Grab is actually good but it's not really the easiest to get your money makers off of.
Spamming fullhop nair on last stock
They're Looking For
Dashdance grab
Flying nair → knockdown
Flying stomp
CC grab
Shield grab / Stomp OoS
Tbh not much else
Stage Position
Edgeguards
If falcon can double jump back to stage with an aerial they probably will. Just do short hop bair in place in the corner to trade/beat the nair.
Level 2 is the start sweetspot double jumping to ledge. You can beat this by runuff sh shining a bit early. Falcon has a pretty good ledge grab box, good hurtbox manipulation, and a low double jump so you have to read their timing. But because he doesn't have shinestall or anything there's really mostly only one timing (they may do something fastfall to mix it up).
On grab
Always upthrow is probably fine
DI out low percent you can go for upsmash
higher percent can do upthrow bair/nair or fair mixup
No DI usually uptilt or upair is good
Fthrow/Backthrow offstage can be good too
Stage Preference
FD
combos are crazy here. No platforms for falcon to rely on.
Fountain
Low platforms mess up so much of falcon's movement. Camp under them.
Yoshi's
Easy to overwhelm falcon here.
Dreamland
I think this is still a very good stage for fox. Platform followups are pretty easy and you'll get kills because falcon is easy to edgeguard.
Stadium
Battlefield
falcon's
At 0%
Dashdance drill stuff
At Mid%
At Kill %
On Shine
Wavedash upsmash usually best
Wavedash grab maybe
Usually don't grab
On Techchase
At mid/high percent techchasing with nair is pretty good and easy. You kind of read tech in place / missed tech by default with a strong nair and then chase down if they rolled with another nair.
Recovering
Going ledge is generally good, but so is recovering really high.