One of the Islamic State terrorists who slaughtered 129 people in Mumbai-type attacks in Paris has been identified by French investigators.

BBC identified him as Omar Ismail Mostefai, a 29-year-old French citizen of Algerian origin with a criminal record. He was known to have been radicalised.

According to French prosecutors, the bloody Friday night attacks on six spots in Paris were carried out by three coordinated teams of gunmen and suicide bombers.

The deadly attack -- akin to the way terrorists from Pakistan ravaged Mumbai in November 2008 killing 166 Indians and foreigners -- also left an estimated 350 people wounded.

Security forces on Saturday said all eight terrorists involved in the well coordinated attacks had been killed.

The Islamic State claimed responsibility for the bloodbath which stunned the world.

Mostefai was reportedly identified after investigators found a severed finger at the scene of the worst atrocity, the Bataclan concert hall where more than 80 people died, BBC reported.

His father and brother have been taken into police custody.

"It's crazy, insane. I was in Paris myself last night, I saw what a mess it was," Mostefai's older brother told AFP before being detained after voluntarily attending a police station on Saturday.

Mostefai came from the town of Courcouronnes, 25 km south of Paris. He lived in the nearby town of Chartres until 2012, according to the local MP and Deputy Mayor Jean-Pierre Gorges, BBC said.

He had a history of petty crime but was never jailed. BBC said the security services deemed him to have been radicalised in 2010 but he was never implicated in a counter-terrorism investigation.

Mostefai's brother said he had not had contact with him for several years following family disputes.

France has begun three days of national mourning.

Friday's attackers targeted a concert hall, a major stadium, restaurants and bars in Paris.

Prime Minister Manuel Valls has said France would continue with air strikes against the Islamic State in Syria.

President Francois Hollande has cancelled his plans to attend the G20 in Turkey.

BBC said investigators were working on the theory that there may have been another team of attackers who managed to flee the scene.

Chief prosecutor Francois Molins told reporters: "We can say at this stage there were probably three co-ordinated teams of terrorists behind this barbaric act.

"We have to find out where they came from... and how they were financed."

Hollande has declared a state of emergency after the Friday horror.

Islamic State said it carried out the attacks on "carefully chosen targets" and were a response to France's involvement in the air strikes on it in Syria and Iraq.