Mehdi Nemmouche, 29, has been in police custody since his arrest on Friday in the southern city of Marseille.
Prosecutors say the repeat-offender has been held under anti-terror laws on suspicion of murder, attempted murder and possession of weapons in relation to the May 24 attack.
Prosecutors said that during an audience before a court in Versailles outside Paris, Nemmouche expressed his refusal to be extradited, when presented with a European arrest warrant.
Nemmouche's lawyer, Apolin Pepiezep, confirmed to Reuters that his client preferred to be judged in France. The suspect has another court appearance on Thursday at which France can however demand that he nonetheless be extradited.
Nemmouche spent five jail terms in France before spending most of 2013 fighting with Islamist rebels in Syria, prosecutors have said. REUTERS