A van has been driven into shoppers at a Christmas market in the French city of Nantes leaving 10 people injured.
In two previous incidents over the weekend, attackers shouted "God is great" in Arabic, raising fears of copycat attacks.
In Nantes, the driver is said to have stabbed himself and officials said he appeared to be unbalanced.
President Francois Hollande has called for an emergency cabinet meeting and urged the public not to panic.
Prime Minister Manuel Valls also called for "cool-headedness".
In Dijon on Sunday, a driver shouting "Allahu Akbar" ploughed his vehicle into pedestrians, injuring 13 people. On Saturday, a man using the same phrase was shot dead by police after attacking them.
Analysis: Hugh Schofield, BBC News, Paris
The French authorities are reluctant to say anything to encourage the idea that there is any kind of pattern behind the three attacks.
For the first incident at the police station in Tours, it is clear that there was a religious motivation. The man left evidence of his conversion to extremist Islamist views.
In Dijon, the man who drove into pedestrians also shouted "God is great" in Arabic. But he is known to have had a history of mental illness. This was not terrorism, is the official line. Similarly in Nantes, there is a strict embargo on speculation about the motives for the attack.
All of which is perfectly understandable. But many people will be asking themselves if there is not some copycat effect being played out. Also, even if it is established the car attacks were the work of unbalanced individuals, might not Islamist propaganda have played some role in pushing them to the act?
Monday's van attack in the western French city took place at about 19:00 local time (18:00 GMT).
According to initial reports, the van drove towards a stall selling hot wine.
One of the traders at the market told local newspaper Presse Ocean: "The white van was speeding towards the customers and onlookers."
After the vehicle came to a halt, the driver stabbed himself several times, causing himself serious injuries, a source close to the investigation told AFP news agency.
The reasons for the attack were not clear, the source said, adding: "As things stand, we have no account pointing to any religious demands."
Speaking in Nantes, Interior Minister Bernard Cazeneuve, said the attacker did not appear to be motivated by politics or religion and seemed to be "unbalanced".
The Christmas market was evacuated and cordoned off by police. A bomb disposal unit was brought in to inspect the van.
In Dijon, the man was arrested after targeting pedestrians in five different parts of the city in the space of half an hour.
The prosecutor in Dijon said the attacker had a long history of mental illness and the incident was not linked to terrorism.
In Saturday's incident, a man stabbed three police officers in the city of Tours before being shot dead.
Anti-terrorism investigators have opened an inquiry into that attack.