However, counter-terrorism investigators are probing the first of three attacks in recent days — the stabbing of police officers that left the suspect dead.
Prime Minister Manuel Valls said there were no indications the car rampages in Nantes and Dijon were linked, but he understood people were worried.
Prosecutors said the attacker in Dijon had been admitted to hospital 157 times. The attack in Nantes “seems to be that of an unbalanced mind”, said another government minister.
On Saturday, an attacker stabbed three officers in Joue-les-Tours before he was shot by police. The attacker’s brother was arrested in Burundi the same day, said Burundi intelligence spokesman Telesphore Bigirimana.
He said the brothers had links to radical Islam and moved between France and Burundi.
In the Nantes attack yesterday, 10 people at a Christmas market were injured when a van driver crashed into the crowd before stabbing himself 13 times.