One has been identified in French media as Ismaïl Omar Mostefai, a 29-year-old Frenchman from the southern Paris suburb of Courcouronnes. He was reportedly identified from police fingerprint records as one of the attackers who blew themselves up at the Bataclan music venue.
Members of his family, including his father and brother, have been detained by police while their homes are searched.
Three other French nationals have been arrested in Belgium, where they all lived, in connection with the attacks.
Mostefai had been flagged as being close to radical Islam, but had never been linked to terrorism.
Paris police said the attackers appeared to be “seasoned, at first sight, and well trained” and were investigating whether they had ever been to fight in Syria.
President François Hollande said the attacks had been “prepared, organised and planned overseas, with help from inside [France]”.