France's president was to lead a crisis meeting of ministers on Friday after a third night of protests over a policeman's killing of a teen saw cars torched, shops ransacked and hundreds arrested.

Police sources said that rather than pitched battles between protesters and police, the night was marked by pillaging of shops, reportedly including flagship branches of Nike and Zara in Paris.

Public buildings were also targeted, with a police station in the Pyrenees city of Pau hit with a Molotov cocktail, according to regional authorities, and an elementary school and a district office set on fire in Lille.

The unrest has come in response to the fatal shooting of 17-year-old Nahel, whose death has revived longstanding grievances about policing and racial profiling in France's low-income and multiethnic suburbs.

The Elysee announced Macron would cut short a trip to Brussels, where he was attending a European Union summit, to chair a crisis meeting on the violence -- the second such emergency talks in as many days.

Around 40,000 police and gendarmes -- along with elite Raid and GIGN units -- were deployed in several cities overnight, with curfews issued in municipalities around Paris and bans on public gatherings in Lille and Tourcoing in the country's north.

Despite the massive security deployment, violence and damage were reported in multiple areas.

Interior Minister Gerald Darmanin said 667 people had been arrested in what he described as a night of violence, while 249 police officers were injured, none of them seriously.

- Macron under pressure -

France has been rocked by successive nights of protests since Nahel was shot point-blank on Tuesday during a traffic stop captured on video.

In her first media interview since the shooting, Nahel's mother, Mounia, told the France 5 channel: "I don't blame the police, I blame one person: the one who took the life of my son."

She said the 38-year-old officer responsible, who was detained and charged with voluntary manslaughter on Thursday, "saw an Arab face, a little kid, and wanted to take his life".

The memorial march for Nahel, led by Mounia, ended with riot police firing tear gas as several cars were set alight in the western Paris suburb of Nanterre, where the teenager lived and was killed.

Heightened security appeared to do little to deter unrest Thursday night.

In the city centre of Marseille, a library was vandalised, according to local officials, and scuffles broke out nearby when police used tear gas to disperse a group of 100 to 150 people who allegedly tried to set up barricades.

Multiple public buildings were also targeted in Seine-Saint-Denis, in the Paris metro area, according to a police source.

In the suburb of Drancy, rioters used a truck to force open the entrance to a shopping centre, which was then partly looted and burned, a police source said.

Firefighters in the northern municipality of Roubaix, meanwhile, dashed from blaze to blaze throughout the night, with a hotel near the train station also catching fire, sending its dozen or so residents fleeing into the streets.

In Nanterre, the epicentre of the unrest, tensions rose around midnight, with fireworks and explosives set off in the Pablo Picasso district, where Nahel had lived, according to an AFP journalist.

The government is desperate to avoid a repeat of 2005 urban riots, sparked by the death of two boys of African origin in a police chase, during which 6,000 people were arrested.

Macron has called for calm and said the protest violence was "unjustifiable".

The riots are a fresh challenge for the president, who had been looking to move past some of the biggest demonstrations in a generation sparked by a controversial rise in the retirement age.

- 'Bullet in the head' -

Nahel was killed as he pulled away from police who were trying to stop him for a traffic infraction.

A video, authenticated by AFP, showed two police officers standing by the side of the stationary car, with one pointing a weapon at the driver.

A voice is heard saying: "You are going to get a bullet in the head."

The police officer then appears to fire as the car abruptly drives off.

Clashes first erupted as the video emerged, contradicting police accounts that the teenager was driving at the officer.

The officer's lawyer, Laurent-Franck Lienard, told BFMTV late Thursday that his client had apologised as he was taken into custody.

"The first words he pronounced were to say sorry, and the last words he said were to say sorry to the family," Lienard said.