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Don't get me wrong, I'll be interested in anything you create. But I think where you can go with F-Zero is quite limited.
Good luck.
Even then, I can't promise a big read, after all despite the greatness of the series, plot and characters weren't exactly a huge feature in the games. More people recognise Captain Falcon from Smash Brothers than from F-Zero! :-S
Still, no harm in going for it.
If you've got a good idea for a story then it could still work.
And if it doesn't, you'll learn for future efforts. :-)
Good luck. :-)