Are there any records or proof of Napoleon being at least part ethnically French, or was he completely Italian/Corsican?
The claim to nobility that Napoleon had was a sketchy one which his father promoted as being Genoan nobility for several generations. So in respect to French bloodlines, there is none. His family was Italian and spoke a Corsican dialect of Italian. When France bought Corsica, they sent a French governor, the Comte de Marbeuf, to claim the island and out down a rebellion by the famed Corsican nationalist, Pasquale Paoli.
The Comte de Marbeuf is important to this because of one reason, supposedly Napoloen's mother, Letizia, had an affair with the Comte but Napoleon insisted this wasn't true because he claims to have been concieved during a siege from French forces.
However, it's all for naught. Napoleon was born a Subject of the French crown and thus a French citizen when the Revolution started. While not of French blood, he belongs to an era where blood matters not but loyalty, something he himself promotes when he tries to integrate the Jewish community into France.