Soldiers of the 93rd Mountain Artillery Regiment managed to avoid the oncoming vehicle in Varces-Allières-et-Risset.
The driver shouted in Arabic at the soldiers before the attack, and sped off afterwards in what reports said was a stolen Peugeot 208.
Reports suggest a woman was also in the car. No one was harmed.
Police tweeted to say a man had been detained in a Grenoble market after a search operation.
The incident comes as victims of a hostage-taking at a supermarket in the south-western town of Trèbes are being buried.
The gunman, Radouane Lakdim, began his attacks on 23 March near Carcassonne by firing at local police officers who were out for a jog, injuring one of them.
French army spokesman Colonel Benoît Brulon confirmed Thursday's attack, saying the man had "verbally threatened" some soldiers who were starting their morning jog, before trying to ram them as they returned.
The 10 soldiers managed to get out of the way of the car, which sped off after the attack.
France remains on high alert after a number of terror attacks in recent years, although in October last year President Macron lifted a state of emergency in place since 2015.
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