Up to 180 millimetres (seven inches) of rain fell in just three hours overnight, transforming the glitzy streets of Cannes, Nice and Antibes into debris-strewn rivers.
In Cannes – home of the glitzy film festival – the torrent carried some cars out to sea, city hall said.
Communications to the region – one of the wealthiest in France, and a magnet for visitors from around the world – were badly hit and thousands of residents were left without power.
Read: Japan evacuates 100,000 in floods sparked by rare torrential rains
President Francois Hollande visited the region, expressing the "solidarity of the nation" to those affected – but also warning that the disaster suggested an environmental message had to be learnt.
"There have always been always catastrophes. But their rhythm and intensity are on the increase," he said, urging that environmental "decisions be taken" as France prepares to host UN-led climate talks in December on a post-2020 pact to curb greenhouse gases.
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.
Rescue teams at Mandelieu-la-Napoule said the water was so murky that it hampered the search for further bodies in underground car parks, where at least seven people died.
"It's apocalyptic," said mayor Henri Leroy. "There are thousands of vehicles. There could be more bodies."
In Cannes, where three people were listed as dead, mayor David Lisnard had tough words for some residents who, he said, were "not always disciplined".
"I'm not judging, because I don't know how I would react in that situation, but it appears we had some people that were very attached to their vehicles when they should have been saving lives."
Nine people were arrested for trying to steal from shops after the storm, he added.
Hundreds of Italian pilgrims returning from the French shrine of Lourdes were trapped overnight as trains were cancelled across the region.
A special track was opened to let the pilgrims, many of them elderly and travelling with doctors, proceed at a slow pace.
The storm "did serious damage to the railway infrastructure, tracks, crossings, electrical lines, primarily around the area of Cannes," a spokesman for French rail company SNCF told AFP.
Around 15,000 homes remained without power after initially 27,000 residences suffered outages affecting some 700,000 people, network authorities said.
Shocked residents gave graphic accounts of the drama.
"I saw water pour in from the veranda. Within five minutes, it was up to my waist," said France Oberlin, a retired resident of Mandelieu-la-Napoule.
"I couldn't open the doors but luckily a neighbour came."
Seated on a plastic chair, surrounded by debris and overturned cars, she looked despairingly at her ground-floor apartment, in which everything had been destroyed.
Around 500 people, many of them British and Danish tourists, were stranded at Nice airport, and a motorway near Antibes was flooded when a small river, the Brague, burst its banks.
A Nice-Nantes match in France's first football division was called off after the pitch became a quagmire.
Nice's mayor's office estimated the city had received 10 percent of its average annual rainfall in the past two days alone.
By dawn, the worst storms had passed over the French mainland and were headed for the Italian coast, Meteo-France said.
The region's worst flood in the past 25 years was in June 2010, when 25 people were killed and there was one billion euros ($1.12 billion) of damage.
In December 1999, 92 people in France were killed by flooding, fallen trees and other storm damage caused by hurricane-strength winds that struck northwestern Europe.
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