President Francois Hollande was expected to visit the site of the disaster, which occurred when the Cote d'Azur received up to 180 millimetres (seven inches) of rain in just three hours.
Three people died when water engulfed a retirement home at Biot near Antibes, and three drowned when their car was trapped by rising waters in a small tunnel at Vallauris-Golfe-Juan.
Other fatalities were reported in Antibes and Cannes.
Rescue teams at Mandelieu-la-Napoule, meanwhile, were searching for six people missing in underground car parks, according to emergency coordinators.
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"Some cars were carried off into the sea," said Cannes Mayor Davis Lisnard, describing water levels reaching halfway up car doors and trees left uprooted on the city's main avenue.
Cannes provided emergency shelter for 120 people, Lisnard said.
"We have rescued a lot of people, and we must now be vigilant against looting," he added.
Speaking on a visit to Japan, Prime Minister Manuel Valls said Hollande and Interior Minister Bernard Cazeneuve were en route to the disaster zone.
Around 27,000 homes remained without power early Sunday, 14,000 of them in Cannes alone.
Communications to the region -- one of the wealthiest in France, and a magnet for visitors from around the world -- were badly hit.
Around 500 people, many of them British and Danish tourists, were stranded at Nice airport.
About a dozen trains were halted at local stations. The state rail company SNCF provided food and blankets to hundreds of passengers who were stuck onboard.
A Nice-Nantes match in France's first football division was called off in the 46th minute after the pitch became a quagmire.