Weather agency Météo France issued weather alerts to another four departments in the south east, taking the total to 19.
All have been placed on orange alert until at least Tuesday morning.
The departments are: Ain, Alpes-de-Haute-Provence, Alpes-Maritimes, Ardèche, Drôme, Gard, Isère, Loire, Haute-Loire, Lozère, Rhône, Saône-et-Loire, Savoie, Haute-Savoie, and Var (see map below).
Hautes-Alpes, Bouches-du-Rhône, Hérault and Vaucluse were added later on Monday morning.
The agency warned that residents could expect “significant damages” from the winds, local disruptions to traffic, and heavy rainfall.
The winds are tipped to reach up to 120 kilometres an hour in some areas.
An orange alert is the second highest warning level the agency issues, and urges the public to be “very vigilant”.
Residents have been warned to beware of falling trees, to keep off roofs, and to avoid secondary roadways.
The areas are on alert until at least Tuesday morning.
Storms lashed much of France over the weekend, and some 70,000 homes – mostly in northern and north western France -were left without power on Sunday.
The coastlines of Brittany and Normandy saw winds of up to 160 kilometres per hour on Saturday night, and the fire brigade in Brittany alone was called out over 600 times, mainly to clear blocked roads.
Meteo-France said storm conditions in the northeastern Atlantic had combined with a strong air stream directed at northwestern France, producing “an event that occurs three or four times per year.”