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.
"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.
"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."
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.
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