The lightning struck in several areas of the Vieux Canal festival in the town of Azerailles.
Officials said the victims were directly hit by the lightning and suffered burns.
Areas in France are often put on high alert at this time of year for violent storms.
The festival’s emergency teams treated those hurt in the incident before they were taken to hospitals nearby.
The rest of Saturday’s performances were cancelled after the lightning strikes. French electronic act Pony Pony Run Run and pop group Black Bones were due to perform.