A van has been driven at shoppers at a French Christmas market in Nantes and the driver is reported to have stabbed himself, officials say, reports BBC News.
Ten people are reported to have been injured, five seriously.
The exact circumstances remain unclear, but the incident comes only a day after pedestrians were run down in Dijon.
The driver of that vehicle screamed "God is great" in Arabic. On Saturday, a man using the same phrase was shot dead by police after attacking them.
Earlier on Monday, French President François Hollande called for vigilance after Saturday and Sunday's attacks, and urged the public not to panic.
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."
The Christmas market was evacuated and cordoned off by police. A bomb disposal unit was brought in to inspect the van.
On Sunday, a driver screaming "God is great" in Arabic ran down pedestrians in Dijon, injuring 11, two seriously.
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.
Read more of this report from BBC News.
See also:
Man shot dead after attacking police station in central France
Driver 'invoking Allah' ploughs into pedestrians in French city centre