Emmanuel Macron has accused protesters of exploiting the death of a teenager shot by police at point-blank range.
At a crisis meeting, France’s president said more officers would be deployed to contain the violence, but stopped short of declaring a state of emergency.
He urged parents to keep rioting children at home and social media platforms to remove certain content.
France has been rocked by three nights of unrest after Nahel M, 17, was killed as he drove away from a traffic stop.
More than 915 arrests were made on Thursday night alone, officials said, and the government announced it would deploy 45,000 police officers in a bid to contain further violence.
Mr Macron said that about a third of those arrested for rioting were “young, or very young”, with Interior Minister Gérald Darmanin later clarifying that some were as young as 13.
Imploring parents to take action, he said it was their “responsibility” to keep any child intending to protest “at home”.
Mr Macron condemned the violence of the last three days “with the greatest firmness” and said Nahel’s death had been used to justify acts of violence – calling it an “unacceptable exploitation of the adolescent’s death”.
He also urged social media companies such as TikTok and Snapchat to take down “the most sensitive types of content” that had been posted, and supply authorities with the names of people using their services to organise violence.
A spokesperson for Snapchat said it had a “zero tolerance” for content that promoted violence and hatred, and would continue to monitor the situation closely.
From Lille and Roubaix in the north to Marseille in the south, shops were ransacked across France on Thursday night, streets were badly damaged and cars set on fire. The interior ministry said there had been more than 3,880 fires on public roads, compared with 2,391 on Wednesday.
Police in Marseille, France’s second-largest city, had already arrested 80 people by Friday evening. It followed more clashes between protesters and riot police.
Public transport halted early in some places and curfews were enforced, with a nationwide curb on buses and trams running from 21:00 local time (19:00 GMT).