Uptilt does a number on falcon. If spaced properly, you can beat out nair sometimes. You can get a lot out of uptilt by being really tricky with your spacing and throwing it out when falcon commits.
I like to play close to falcon and play a game of trying to read/catch their jump with a quick upair/uptilt and jabbing/spotdodging their grab attempts (or wavedashing back). If you can get a falcon cornered, then it becomes rock paper scissors at that point. Just be wary of his instant upair OOS, if he tends to do them.
Also, I find that falcon (or at least many of the falcons I've played) have trouble when you put aerials out above their shothop nair range. Like Plunder said, fullhop nair is great. Even a falling AC bair really close to their dash dance into pivot jab and bait and catch their jump.
Like a lot of mario's matchups against characters that tend to control the neutral, the falcon matchup feels centered around baiting and acting swiftly OOS. In a lot of matchups, I think short hop forward -> waveland back is super good as a bait and usally puts you in a good position to punish their reaction to your fake commitment.
Full hop fireball waveland and just fireballs in general have felt really risky in this matchup for me. Falcon tends to run below, jump over, or sometimes cancel out mario's fireballs. On larger stages, you can get away with one if you think they aren't going to run in. If they do run in, you can waveland, upair, nair, or double jump after a fullhop fireball. I find fullhop fireball, fade back into upair (right before you hit the ground) a really good mixup. People don't expect you to have a hitbox there so it gives you free openings sometimes.
When you do get in on falcon, the biggest concern is ending your combos at the right time without allowing him to get away with DI out. At mid/lowish percents, don't try to chain many upairs. Sometimes DI out will also make it so you can't uptilt after your upair. The best thing to do, from what I currently understand, is to finish with dsmash or ftilt after getting an upair at low/mid percent, because that works with any DI.
Also, while approaching with short hop bair/upair, you can double jump and waveland or a platform before you hit the ground.
It's my fav thing right now. Looks stylish af and it's not too difficult.
Idk, that's all I got for now. Sorry if there's any typos. I wrote this pretty late at night. I'll check it over later.