Three people were injured on Monday evening after being attacked by a man with an axe in a Lidl supermarket in Jeumont, northern France, Reuters reported, citing local daily La Voix du Nord.
Two of the victims are understood to be seriously injured following the attack with the third's injuries thought to be less severe.
Jeumont is located close to the Belgian border.
The man later turned the axe on himself and also was seriously injured, according to reports.
There were no immediate details on the motivations for the attack and it is unclear whether it is terror-related, but France has been on high alert in recent years after being hit by a number of terrorist attacks.
The most notable of these was the attack in November of 2015 in which 129 people were murdered and which was claimed by the Islamic State (ISIS) organization.
At the start of 2015, 12 people were murdered in an attack on the offices of the satirical magazine Charlie Hebdo attack.
Following the Charlie Hebdo attack, a man linked to ISIS shot and killed a policewoman in a Paris suburb before taking hostages at the Hyper Cacher kosher supermarket the following day, killing four more people.