"Mehdi Nemmouche was informed of the decision of the court of appeal in Versailles on Thursday and he filed an appeal notice the same day," lawyer Apolin Pepiezep told AFP.
Nemmouche, who was detained several days after the attack in which four people died, will now have 15 days to challenge the ruling. A final decision must then be made within 40 days.
"We are contesting the decision to show that the court of appeal hasn't applied the law," Pepiezep said.
The court ruled on Thursday that Nemmouche, who spent more than a year fighting alongside radical Islamists in Syria, should be handed over to the Belgian authorities for killings "with a terrorist connotation."
According to Walla! News, Pepiezep added that while Nemmouche's primary concern is the extradition to Belgium, he would also be fighting any potential extradition attempts to a third country: Israel, the home of two of his victims. The legal team reportedly received guarantees that Nemmouche would not be extradited to any country other than Belgium, but have not seen written evidence that that request was accepted by the court.
Nemmouche was arrested on May 30 in the southern city of Marseille in a bus coming from Brussels during a random check by customs officials.
He had in his possession a revolver and a Kalashnikov rifle - the weapons believed to have been used in the shooting - as well as a portable camera with which he is thought to have attempted to film the attack.
Tel Aviv natives Emmanuel and Miriam Riva were killed in the May 24 shooting, as was a French woman and Belgian man.