The appeals court in Rennes, western France, said that Mario Miceli, 62, would be handed over to Italian authorities, though the decision could still be appealed.
Miceli had been living under his own name in Arzon, a town perched on the Quiberon Bay, since arriving in 2018.
He became the target of a European arrest warrant after a Milan appeals court convicted him in January on charges of association with criminals and extortion.
Police said Miceli, a member of the 'Ndrangheta mafia, did not try to resist his arrest on September 4.
According to the Corriere della Sera newspaper, he belongs to the Barbaro-Papalia clan, and is a son-in-law of the mafia boss Domenico Papalia.