Learning how to utilize Nairs for Falcon is one of the many attributes that set Falcons apart. You could try to use a Nair as an approach, but mind you it can easily be block, if seen coming, and Falcon is an easy character to combo off of.
A sweet combo to pull off is Nair (once or twice) and then the knee. You don't have to necessarily do the Dair, Side B, and then this. Side B is like a coin toss, it can be extremely rewarding especially if it leads into a knee, but more than likely will be bad for you, if missed/blocked.
You can use a SH Nair to jab the opponent and then back away with the 2nd leg, or to space forward with both of them. Again though, if blocked or dodged you will instantly have to put on your shield or be prepared for rushed attack or a projectile. In other words it's not a very good approach.
Nairs in the air are good if your opponent is rushing you down with projectiles (Falco jumping a lot)
You could do a one full jump-not fast fallen Nair, and if you nick them, respond with a Uair with your second jump.
The Up air is another tool that sets Falcons apart. That foot.
Speaking of fast falling though, it becomes a great tool in your air game, and some what for recovery (given how predictable it is)
Dairs in the air are good for the length, strength, given that you can pull of many (if needed) while in the air.
Falcon is like a character that pokes his opponents offensively or defensively. Doing what he can to fight against projectiles, or making the characters come to him. All of those pokes can lead to combos which is the core of any Falcon player.
Another core feature of any Falcon player is speed. And I'm not talking about his blunt speed, but the things that make him speedier.
L-Canceling. I'll tell you like it is, and say that any good Falcon player will successfully L-Cancel all his moves that can, and even more so when they're fast fallen. It's what makes him so unpredictable. You have to do that with Falcon or you will be targeted and juggled to death. When you have a Falcon moving as fast as it is, sending out so many moves from the sky, to the head, etc, when they're all L-Canceled it really makes a difference in your rush down, and the opponents ability to hunt you down.
Wavedashing out of (The term that refers to running back in forth in a set zone) plus moonwalking (For bonus points
) Adds to this unpredictability factor, thhat should be in your favor, if you don't get hit.
So if you really want to be good with Captain Falcon or any character really. Learn how to L-Cancel their moves (Some moves take more priority over others), and learn how to wavedash on command (In C. Falcon's case, it's not as crucial though). L-Canceling his Dair is very important, you will see why you would rather want to keep throwing out Dair instead of Nairs. The reward, the risk, all of it favors Dair over Nair.
One more tip is to learn how to Knee out of the ledge.
Another thing, learn how to gentleman and follow with either a knee, a diagonal to the right A, or a down tilt (These steps are ordered by priority, it all depends on percent) If anything though, learn how to do a 1-2 punch followed by a grab at low percentage, if they're too high in percent and move out grab range than resort back to the above.
Yes I am a Falcon main, and all of this was on top of the head. If any more info comes I'll be sure to edit it in my post.
I hope this helps. The road for Falcon players is an upward battle in Project: M
Take care.
-Vic