Three elderly people drowned when their retirement home near the city of Antibes was flooded.
Others died trapped in their cars in tunnels and underground car parks as the waters rose.
President Francois Hollande announced a state of “natural disaster” in the affected region.
He thanked rescuers and expressed the “solidarity of the nation”.
Framcois Hollande offered condolences as he visited the retirement home in the town of Biot and urged residents in the region to remain cautious, saying: “It’s not over.”
Heavy rain hit the French Riviera on October 3.
The city of Nice is estimated to have received 10% of its average yearly rainfall in two days alone.
The river Brague burst its banks, sending water coursing into nearby towns and cities. Social media pictures showed water gushing down the streets of Cannes.
Cannes mayor David Lisnard said: “Some cars were carried off into the sea. We have rescued a lot of people, and we must now be vigilant against looting.”
Eric Ciotti, president of the Alpes-Maritimes department, tweeted: “We have lived through an apocalyptic situation that we have never experience before.”
The main highway through the area has been closed, trains halted and hundreds of tourists sought shelter at Nice airport overnight. About 10,000 homes were still without power on October 4, mainly in Cannes.
Some concertgoers attending a show by rock legend Johnny Hallyday at a venue in Nice had to sleep overnight there after becoming stranded.
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