By Marine Pennetier and Gilbert Reilhac

PARIS, WISSEMBOURG, France (Reuters) - The third man who attacked the Bataclan concert hall in Paris on Nov. 13 has been identified as a 23-year-old French national who went to Syria two years ago, according to officials involved in the inquiry into the multiple attacks on the French capital.

Investigators identified Foued Mohamed-Aggad as one of three Islamist gunmen who killed 90 people at the Bataclan after his mother told them that she had been informed of his death by text message from Syria, a lawyer for the dead man's family said.

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

Officials have yet to put names to all of eight dead gunmen and suicide bombers directly involved in last month's attacks, for which Islamic State, a militant group that controls swathes of Syria and Iraq, claimed responsibility.

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, who said the woman got the text message 10 days ago.

"She was instantly struck by the horrific thought that he might have been one of the Bataclan suicide attackers," said Cotta, adding that she was asked by the dead man's mother to get in touch with investigators.

Mohamed-Aggad went to Syria in late 2013 with a gang of others from his neighborhood 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, where 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.

TRIED POLICE, ARMY, BEFORE JIHAD?

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In Mohamed-Aggad's home town of Wissembourg, about 70 km north of Strasbourg and near the German border, some people who knew him were surprised to learn of his role.

"I can't believe it was him," said Yazar Mesut, a 46-year-old neighbor, speaking in one of the town's bars. "He was intelligent and polite, knew what respect was about and didn't act like a big shot."

Wissembourg and Strasbourg are part of the eastern region of France, one of six of 13 regions where the National Front with its anti-immigrant policies is leading after the first round of elections last Sunday.

According to another neighbor who gave his name only as Youssef, the young man failed the police entrance exam by just a few points and was also refused by the army.

"That's the only time I saw him disappointed. He was complaining. He reckoned it was because of his foreign origins," said Youssef.

Mohamed-Aggad's Moroccan-born mother had raised the two brothers and a sister on her own after a divorce from her husband of Algerian descent about 10 years ago, he said.

Wissembourg council and the Strasbourg prosecutor would not comment on Youssef's claims.

According to Christian Mahler, who lived on the same floor in the building near Wissembourg station where the family lived for a time, Mohamed-Aggad began frequenting the Mosque more often around 2012.

Can Yakup is president of a Turkish cultural center that he said Mohamed-Aggad visited "once or twice".

"The last time I sent him away because he wanted to pray on his own," Yakup told Reuters.

The Bataclan shootings were part of a co-ordinated attack 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 Nov. 13 attackers, Abdelhamid Abaaoud, 28, a Belgian of Moroccan origin who died in a police raid the following week.

Another Nov. 13 attacker, Salah Abdeslam, 26, French and born in Brussels, is still on the run.

(Writing by Andrew Callus and Brian Love; Editing by Catherine Evans)