The French government has denied any links between three attacks in as many days, including two nearly identical rampages by drivers who ploughed into holiday crowds, but announced plans to further raise security in public spaces.

Prime minister Manuel Valls said the attacks were unrelated to terrorism. Lamenting "the ravages of propaganda on fragile minds," he urged France to remain calm and avoid overreacting to isolated incidents.

In the western city of Nantes last night, a van burst into a Christmas market, injuring 10 people before the driver began stabbing himself. The night before, in the eastern city of Dijon, a driver reportedly shouting "God is great" in Arabic ran down several people, injuring 13 before coming to a stop.

Those incidents came after an attacker knifed three police on Saturday before he was shot dead by one of the officers. The man's brother was arrested the same day in Burundi, their homeland. French counter-terrorism investigators were called in to the case.

"These three events have no link," French President Francois Hollande said.

The drivers in the attacks in Nantes and Dijon had long histories of mental illness, officials said.

Mr Valls said there were no ties with terrorism in the attacks, but announced that security would be increased in public spaces during the holidays.

In Nantes, bystanders ran toward the attacker as he was stabbing himself, said Mohammed Bader Ghegate, one of the witnesses who ended up at the man's side. He denied reports that the attacker said "God is great" in Arabic.

"I said that to myself: 'Allahu Akbar, help us so there is no bloodshed'," Mr Ghegate said.