Hailstones the size of tennis balls were reported in Seine-Maritime on the Channel coast, where 200 homes and business premises were flooded and cars damaged.
There were power cuts in Aquitaine in the south-west, Limousin in central France and Normandy in the north, leaving 60,000 homes without electricity overnight, although most had power restored during Sunday morning.
As millions of French people started their summer holidays, jazz festival in the Bordeaux town of Saint-Emilion was called off on Saturday evening and Sunday with about 1,000 spectators being moved out of the area.
An appearance by singer Vanessa Paradis was also cancelled when the Festival du Grand Souk in the Dordogne was scrapped at the last minute.
Traffic on the high-speed TGV service between Bordeaux and Toulouse was disrupted due to a power failure.
Summer camps of the boy scout movement suffered, too.
Three camps in the south-west were evacuated overnight and six scouts bivouacking in Charente-Maritime were taken to hospital with minor burns after being struck by lightning.
The storms moved east on Sunday and were expected to peter out overnight, except for in Lorraine and Champagne-Ardenne, although weather service Météo France warned of the danger of flooding from the Alps to the Vosges in the east of the country.