The Météo France weather service has issued an Orange warning for several départements in the east and south of France - the agency's second highest warning level.
It forecast "violent" and "dangerous" storms that are expected to bring downpours of up to 50 millilitres in some areas.
The départements affected are Ain, Ardèche, Doubs, Drôme, Isère, Jura, Loire, Haute-Loire, Lozère, Rhône, Saône-et-Loire, Savoie, and Haute-Savoie.
The agency predicted that the storms would hit at around 2pm on Monday and last until at least 6am on Tuesday.
The agency said that the "violent" storms may well cause damage to properties in the affected areas, and warned residents to be cautious if travelling, and to avoid the use of telephones and electricity.
Elsewhere in France, Monday will bring mostly good summer weather.
Temperatures will be in the low to mid-twenties going into the afternoon an evening across most of France, with storms set to move in to the south west, and showers predicted for the north west.