A total of 34 departments are on Orange alert - the second highest level of weather warning - for violent storms, high winds, downpours, avalanches and high coastal waves.
The are advised to take precaution and avoid any unnecessary journeys.
On Sunday northern France was hit by fierce storms which left 20,000 homes without power an forced ferry to run aground in the port of Calais.
According to the latest figures by energy providers Enedis, some 120,000 homes were without power on Monday, including 90,000 in the Pays de la Loire.
On Monday the north including the departments of Pas-de-Calais and Somme could see snowfalls.
In the west storm Ana will see winds reach up to 130 km/h in certain areas along the Charentes Maritimes coast. Those living in Nouvelle Aquitaine region of the south west have been warned to expect huge coastal waves.
In the east there will be heavy rain and high winds and the Alps should see some heavy snowfalls above 1,500m in altitude with gale force winds.
The Mediterranean coast will also be hit by high coastal waves which could cause flooding inland. The public are advised to avoid venturing near the water.
The map below shows which parts of France are on alert for which kind of extreme weather.