The incident took place in the town of Varces-Allieres-et-Risset on Thursday morning, according to local newspaper Dauphine Libere, which initially broke the story.
A group of soldiers from the 93rd Mountain Artillery Regiment had just started jogging when the vehicle rushed towards them, France Bleu said. The servicemen managed to escape by jumping into a nearby ditch.
The driver “deliberately drove” the Peugeot car into the group of soldiers, Le Dauphine said, citing its sources. BFMTV reported that the driver attempted to hit the servicemen at least twice before speeding away.
“A person tried to run down two soldiers from the 93rd Mountain Artillery Regiment in Varces, for unknown reasons,” a source close to the investigation told Reuters.
“Given the context, the incident is being taken seriously but we don't know his motivations.”
According to witnesses, the driver “insulted” the soldiers before fleeing.
The incident in Varces comes nearly a week after the tragedy in the towns of Carcassonne and Trebes, which left four people dead.
The Islamic State-inspired gunman, Redouane Lakdim, opened fire from a stolen vehicle at several jogging officers, before storming a supermarket. He was killed following a stand-off with police.