Ninety people were killed at the Bataclan during last month’s attacks.
The AFP news agency and Le Parisien newspaper identified him as Fouad Mohamed-Aggad, 23, from Strasbourg, citing police sources.
They reported he had travelled to Syria as part of a group of radicalised youth in late 2013.
Several of the group, but not the Bataclan bomber, were later arrested upon returning to France, Le Parisien said.
Two others who blew themselves up at the music venue were identified as Frenchmen Omar Ismail Mostefai, 29, and Samy Amimour, 28.
Mostefai was identified from a finger-tip found at the venue, where US band Eagles of Death Metal had been playing a concert when the gunmen attacked.
He was reported to have previously worked as a banker in Chartres near Paris but in 2010 was identified by authorities as a suspected extremist.
Amimour, from the north-eastern Paris suburb of Drancy, had been charged with terror offences in 2012 over claims he planned to travel to Yemen.
After being placed under judicial supervision, he disappeared, with authorities issuing an international arrest warrant.
BBC
