The president visited the site of the disaster, which occurred when the Cote d'Azur was lashed by to 180 millimetres (seven inches) of rain in just three hours.
"The toll is not yet final. In these moments, we must be fast, efficient and coordinated," said Hollande.
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 said the water was so murky that they could not see the bodies trapped in underground car parks, where at least seven people died.
"It's apocalyptic," said mayor Henri Leroy. "The parking was half-emptied but there are thousands of vehicles. There could be more bodies."
Fire engines were busy sucking water out of underground parkings and basements.
"I saw water pour in from the veranda. Within five minutes, it was up to my waist," said one retired resident, France Oberlin, still in shock.
"I couldn't open the doors but luckily a neighbour came," she said.
Sat on a plastic chair, surrounded by debris and overturned cars, she looked despairingly at her ground-floor apartment, in which everything has been destroyed.
(A flooded road in Biot, southeastern France, on Sunday. Photo:AFP)
Vigilant against looting
Water coursed through Cannes, Nice and Antibes, transforming the streets of three of France's most glamorous cities into debris-strewn rivers.
"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.
Hollande issued a message thanking rescuers and local officials and expressed the "solidarity of the nation" to those who had been affected.
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.
The A8 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 in the 46th minute 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.
The worst national toll from flooding over this period was in January and February 1990, when 81 people were killed by violent storms in the north and west of the country.
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.