"The lightning struck in several areas during" the Vieux Canal festival in the northeast town of Azerailles, the regional council said in a statement.
A woman in her 60s and a 44-year-old man were said to be in serious condition after being struck. The victims were "directly hit by the lightning and suffered burns".
According to local media, lightning struck a big tent under which festival goers had taken refuge, which was located near a large tree.
Those injured received first aid from the festival's emergency centre before being taken to hospitals in the area.
Two children aged about 10 were also taken to hospital after suffering shock.
All Saturday evening concerts have since been cancelled, local reports said.