Nintendo

...That sounds kind of amazing. I don't know how happy F-ZERO fans would be with that, but Smash gave Captain Falcon enough fighting moves that it could kind of work.

The focus should stay on the racing. The mechanics need to be solid, there needs to be enough tracks, the works. The singleplayer would need to primarily be about racing, since it's rare that a game can be two genres at once and succeed. But the structure can be flexible!

You play as Captain Falcon in a somewhat open world. You can drive around freely in the Blue Falcon. The world is very large, but the Falcon is very fast so it's fun to explore. There are oodles of races to be had, but you have to drive to them in order to participate. At any point you can hop out of the Blue Falcon and, like, start punching stuff. Captain Falcon runs pretty fast, has his Falcon Punch, has most of his moves from Smash and more. You could also tweak the Blue Falcon's stats and look as you go. It would still be the racing game that F-ZERO fans want, but it would also attract people who weren't interested in F-ZERO but like Captain Falcon in Smash and want to play as him rather than his vehicle.