Named Alex, the storm brought fierce winds and torrential rain.
A number of villages north of Nice in France suffered serious damage from floods and landslides, with roads, bridges and homes destroyed.
In north-western Italy, flooding was described as "historic". A section of a bridge over the Sesia river collapsed.
French Prime Minister Jean Castex has deployed the army and released emergency funds to tackle the worst floods for decades in south-eastern France.
Up to 20 people are either missing or have not checked in with relatives.
