Hundreds of people marched on Monday in support of a French mayor whose house was attacked by a burning car, as the country entered a second week gripped by violent protests and riots.

A large crowd in L'Haÿ-les-Roses, a suburb of Paris, showed solidarity with Mayor Vincent Jeanbrun, whose house was rammed by the vehicle early on Sunday morning.

The gathering came after a calmer night in the country, which has been racked by angry protests since a police office shot and killed a 17-year-old boy at a traffic stop last Tuesday.

Jeanbrun's address was well known in the community before the attack, CNN affiliate BFMTV reported. The incident injured his wife and one of his children, Jeanbrun said earlier, calling it an assassination attempt.

Locals and officials held up a banner at the march reading "Together for the republic!" Jeanbrun, dressed in the sash of the French tricolore, told supporters: "I have only one word: thank you.

"Democracy was attacked," he said. "More than ever, our republic and its servants are threatened and attacked," he added.

In a previous statement on Sunday, the mayor said that while he was at city hall, "individuals rammed their car upon my residence before setting fire to it to burn my house, inside which my wife and my two young children slept."

"While trying to protect the children and escape the attackers, my wife and one of my children were injured," he said, adding that he had "no words strong enough to describe his emotion towards the horror of this night."

France's Ministry of Interior said 157 people were detained overnight into Monday morning, down from more than 700 the night before.

Three police officers were injured, a police station was attacked and 352 public roads were set on fire, but BFMTV reported that "no major incident was reported" overnight.

French President Emmanuel Macron will launch a procedure to "understand deeply" the cause of unrest that has been rocking France over the past week, a source present at the meeting between Macron and his top officials on Sunday told CNN.

Macron told ministers present to continue to "do everything to establish order," the source said.

The wave of protests started after a police officer shot dead Nahel Merzouk, 17, during a traffic stop. The officer accused of the shooting has been charged with voluntary homicide.

Merzouk's grandmother appealed to protesters on Sunday, telling BFMTV: "They should not damage the schools, not break the buses, it was the moms who take the buses.

"I'm tired," the grandmother, identified by BMFTV as Nadia, said, adding that Nahel's mother "doesn't have a life anymore."

The teenager's funeral took place on Saturday at a mosque in Nanterre, the Paris suburb where he was killed.