Work on your movement and beat him in the neutral game every single time. Falcon IMO has a better combo/punish game, but your neutral is stronger. I try to aggressively space my dash dance around him, and since most falcon's like space to do their SHFFL approaches, they'll feel uncomfortable with such a short distance and they'll do something punishable. If he rolls or spot dodges, that's all reactable/punishable with a grab. If he attacks you, you can shield then respond with a grab or wavedash out of shield accordingly. You can up tilt his approaches too, but don't do it too much, he might just be baiting you out and punish the lag. If he tries to grab, you just need to adjust your dash dance a little. If he starts to dash dance then you can dtilt to make him respect your dash dance's range. If he tries to work the platform game in neutral, then it's no longer neutral and you have the advantage, since he's now vulnerable to your marth utilt/uair shenanigans.
Once you get grabs off dash dance, I usually go for down throw tech chases. If you're by a ledge and your down throw sends him towards the ledge, you can do a frame trap by turning around and dtilting immediately after your throw (if you're used to doing this against lighter characters, you have to wait a little longer, falcon is heavy). This covers tech in place, no tech, and tech away can be reacted to easily. If he techs in then you get a free grab if you turn back around and you can start the thing over again. You can mix up fthrow regrabs/tech chases as well, especially at 0 if they expect the dthrow instead.
Once you build some percent on grabs/tech chases up to like 40, you can start to up throw instead and do utilt, and up air stuff. Don't spend too much time trying to juggle him though, get him off stage once you think he's at a high enough percent, or just get him off right away if you think you can do it. Falcon is super easy to edgeguard, so it's worth it sometimes to end your big fat combo early. I usually do reverse nairs through platforms or try to corner him with my dash dance and hit him off stage with a fair, nair, or dtilt.