On the contrary, I live in a weird country, we've been taught we write Napoleon's name like this, and we always - except foreign names - write surname before the first name, so I wasn't sure.
He was born in Corsica, which was part of the Republic of Genoa since 1282. But the French bought and annexed Corsica to their territory in 1768. Since 1768, Corsica was officially France. Napoleon Bonaparte was born in 1769, probably less than a year after that. So, yes. He's French.