A judicial official said that 29-year-old Frenchman Ismael Mostefai had been flagged for links to Islamic radicalism.
Mostefai’s father, a brother, and other family members have been detained and are being questioned.
The mayor of the French city of Chartres, Jean-Pierre Gorges, identified Mostefai as a resident in a Facebook post.
The Paris prosecutor said one of the attackers was a 29-year-old Frenchman born in the Chartres region who had been known to authorities for radicalism.
The prosecutor said he was identified by fingerprints on a finger found in the carnage of the Paris attacks Friday night, which left at least 132 dead and hundreds wounded.
In Belgium, an official said two of the seven attackers who died in Paris on Friday night were French men living in Brussels, one of them in the neighbourhood of St Jans Molenbeek.
The Islamic State (IS) group has claimed responsibility for the attacks.
The arrests came as the authorities stepped up their hunt for accomplices of the extremists responsible for a gun and bomb rampage targeting the vibrant cafes, bars and clubs of Paris.
French President François Hollande vowed France will wage “merciless” war on IS after the jihadists claimed responsibility for the attacks.
A French judicial official says a Seat car with suspected links to the attacks has been found by police in Montreuil, a suburb about four miles east of Paris.
The official could not immediately confirm if it was the same black Seat linked to the gun attacks on the Le Carillon bar and the Le Petit Cambodge restaurant in Rue Alibert in the city’s 10th district.
Grief, alarm, and resolve spread across Europe as officials raced to piece together information on the attackers.
Paris prosecutor Francois Molins said three groups of attackers, including seven suicide bombers, carried out the “act of barbarism” that shattered a Parisian Friday night.
A Syrian passport found near the body of one was linked to a man who entered the European Union through a Greek island last month.
Mr Molins said that as well as the 132 people who were killed, 352 people were injured, 99 critically.
He said the attackers in the Bataclan concert hall, where 89 people died, mentioned Syria and Iraq during their rampage.
Seven attackers launched gun attacks at Paris cafes, detonated suicide bombs near France’s national stadium and killed hostages inside the concert venue during a show by an American rock band.
Late on Saturday, a crowd of up to 250 people gathered for an impromptu candlelight vigil at the Place de la Republique, the site of a massive demonstration in the wake of the Charlie Hebdo killings earlier this year.
Adrien Chambel, a 27-year-old law student, said the crowd was much sparser than in January. “You feel that people are petrified,” he said.
Mr Hollande, who declared three days of national mourning and raised the nation’s security to its highest level, called the carnage “an act of war that was prepared, organised, planned from abroad with internal help”.
The president said France would increase its military efforts to crush IS.
He said France — which is part of a US-led coalition bombing suspected IS targets in Syria and Iraq and also has troops fighting Islamic militants in Africa —“will be merciless toward the barbarians of Islamic State group”.
IS claimed responsibility in an online statement in Arabic and French circulated by supporters.
It was not immediately possible to confirm the authenticity of the claim, which bore the group’s logo and resembled previous verified statements from the group.
The statement called Paris “the capital of prostitution and obscenity” and mocked France’s air attacks on suspected IS targets in Syria and Iraq, saying France’s air power was “of no use to them in the streets and rotten alleys of Paris”.
Many of Paris’s most famous tourist attractions closed down on Saturday, including the Eiffel Tower, the Louvre Museum, and the Disneyland theme park east of the capital.
Some 3,000 troops were deployed to help restore order and reassure a frightened populace.
French interior minister Bernard Cazeneuve announced that all public demonstrations would be banned until Thursday and local governments throughout the country would have the option to impose nightly curfews.
Parisians expressed shock, disgust, and defiance in equal measure. Some areas were quiet, but hundreds queued outside a hospital near the Bataclan concert hall to donate blood.
As a shrine of flowers expanded along the pavement, a lone guitarist sang John Lennon’s peace ballad ‘Imagine’.
The authorities said seven attackers died, six in suicide bombings, a new terror tactic in France. They said police shot the other assailant, exploding his suicide vest.
Mr Molins said all seven attackers wore identical suicide vests containing the explosive TATP.
The owner of the passport entered the EU in October through Leros, one of the islands that tens of thousands of people fleeing war and poverty in Syria and elsewhere have been using as a gateway.
Mr Molins said the Syria-linked attacker was not known to French intelligence services.