The town is currently under a coronavirus lockdown, although people are allowed out to buy essentials.
The attacks took place in the morning outside a bakery where customers were queuing, and at shops in the town center, according to Mayor Marie-Hélène Thoraval, who said the assailant had been arrested.
Witnesses told the Reuters news agency that the man struck at random and in several places while moving around the town center.
It was not immediately clear if the attacks had any link to the lockdown. Interior Minister Christophe Castaner said security services were trying to establish the nature and circumstances of the incident.
