Those injured include children who were in a tent during the storm.
The victims were "directly hit by the lightning and suffered burns", the regional council said.
A woman in her sixties and a 44-year-old man are reported to be in a serious condition as a result of the strikes.
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Parts of France around this time of the year are often put on alert for violent storms.
Those hurt in the latest incident received first aid from the festival's emergency teams before going on to get treatment from local hospitals.
All of Saturday's performances were cancelled after the incident. Among those due to appear were French electronic act Pony Pony Run Run and pop group Black Bones.
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