French police have identified the first attacker involved in a series of assaults across Paris, which left at least 129 people dead and wounded hundreds more.

Omar Ismail Mostefai was a 29-year-old Paris native whose detached finger was found overnight at the Bataclan concert hall, the scene of the bloodiest attack, the AFP news agency said.

The French citizen had been known to police for his alleged links to armed groups but had not been previously linked to violent activities.

French authorities believe the attacks were planned abroad by the Islamic State of Iraq and the Levant (ISIL) group, but have not yet confirmed the identities of others involved.

ISIL purportedly claimed responsibility for the attacks shortly after the incident but has also not revealed the identities of the attackers.

Investigators in France, Belgium, Greece and Germany are trying to identify the seven attackers and their accomplices.

In Belgium, police arrested several people over their alleged links to the attacks. Koen Geens, Belgian justice minister, said those arrested were detained in connection with a grey Volkswagen Polo that was rented in Belgium but found near the scene of the attack.

Witnesses said some of the attackers arrived in a car carrying Belgian plates.

Greek authorities have also confirmed that a man who died in the attacks with a Syrian passport found next to him had registered as a refugee on the island of Leros in October.

Police said the passport had been found near the body of one of the attackers.

German police arrested a man on November 5 after machine guns, hand guns and explosives were found in his vehicle during a routine check on a motorway.

Horst Seehofer, Bavaria's state premier, said there was reason to believe he had links to the attackers, and that the case "shows how important it is for us to have some clarity on who is in our country".

The attacks have intensified debate on Europe's response to the refugee crisis. Marie Le Pen, the leader of France's far-right National Front party, has called for a tightening of the country's borders.

Al Jazeera's David Chater reporting from Paris said security services will be concentrating on how the perpetrators were able to get themselves and their ammunition into the country without being noticed.

"The intelligence services will be looking at the blind spots in their system that allowed ISIL to get through their net- exactly where did they get their weapons, how did they get their ammunition, and has the Schengen system made the whole of Western Europe vulnerable.

The attacks have also led to an outpouring of solidarity among France's allies, with thousands attending marches and memorials outside French embassies and consulates across the world.