The Météo France weather service put Paris and the surrounding region on orange storm alert on Saturday afternoon, warning that the bad weather could continue through to Sunday night.
Most of western and northern France was on alert on Saturday and Sunday, although the south-east and the Mediterranean coast were expected to enjoy sunshine.
In storm-hit areas the forecasters said there could be hail and winds up to 90 km/hr and warned people not to use phones or other electrical equipment when there was danger of lightning.
Four people died this week in storms that caused flooding and damage to property.
Over the past 12 days rescue services have been in action 7,900 times across France, according to the interior ministry.