The third Bataclan attacker has been identified by French police as a 23-year-old French national who went to Syria two years ago but was not picked up by intelligence as a threat on his return. 

Investigators named Foued Mohamed-Aggad from Strasbourg as one of three gunmen who killed 90 people at the Bataclan in Paris last month after his mother told them that she had been informed of his death by text message from Syria.

Two of the three attackers killed themselves by exploding their suicide vests and another was shot dead by police.

They managed to identify Mohamed-Aggad after being alerted by his mother and then matching her DNA to his.

"The SMS message told her that her son had died, saying: 'He died on November 13 with his brothers," said Francoise Cotta, lawyer for the mother and her family.

"She was instantly struck by the horrific thought that he might have been one of the Bataclan suicide attackers," said Cotta.

Mohamed-Aggad went to Syria in late 2013 with a number of others from his neighbourhood in an area outside the eastern French city of Strasbourg. Seven of the group were arrested in May 2014 after returning to France.

It remained unclear when and how Mohamed-Aggad returned to France and intelligence services are under scrutiny over their monitoring of the movements of home-grown jihadists.

His older brother Karim, who also went to Syria, is in jail in France, the officials said.

The Bataclan shootings were part of a co-ordinated series of attacks in Paris in which assailants killed 130 people at a string of cafes, near a sports stadium and at the Bataclan.

The other two attackers at the concert hall have been named as Samy Amimour, 28, from Drancy, north east of Paris, and Ismail Omar Mostefai, 29, a Frenchman of Algerian descent who lived for a time in Chartres, south west of Paris.

Amimour also spent time in Syria, as did the presumed ringleader of the November 13 attackers, Abdelhamid Abaaoud, 28, a Belgian of Moroccan origin who died in a police raid the following week.

Another of the attackers, Salah Abdeslam, 26, French and born in Brussels, is still on the run.

Officials have yet to put names to all of eight dead gunmen and suicide bombers directly involved in last month's attacks, for which ISIS have claimed responsibility.

Additional reporting from Reuters