Well, if they're spamming projectiles, they're not faster than you (since Sonic is the only character faster than Falcon), so my first recommendation would be to try to keep things close. If they run from one side to the other spamming projectiles and get away from your rushdown by rolling, you should be able to punish that too.
Another thing to keep in mind is that lots of projectiles can be shorthopped, so approaching with shorthop nairs can sometimes be a decent plan, especially since you can often go from nair->jab before they have time to throw out another move.
Finally, recall that Falcon's jab has a slight disjoint, which means there's a number of projectiles you can cancel simply by jabbing, which can help you close the distance.