The heaviest death toll was in the town of Mandelieu-la-Napoule, where eight people were found dead as of midday Monday. All perished trapped in underground car parks of several houses, officials said.
Heavy flooding along the Côte d'Azur saw the River Brague burst its banks close to the city of Antibes and sent waves crashing into a nearby retirement home where three people drowned.
Two Germans are missing near the city of Antibes while another two, whose nationalities have not been confirmed, are missing in Cannes.
Rail services continued to see interruptions Tuesday, while more than 1,800 homes remained without electricity.
The national railway company SNCF said it expected a gradual return to normal service by Saturday at the earliest.
Emergency services and residents of the most affected towns - Cannes, Antibes, Mandelieu-la-Napoule, Biot, Vallauris and Mougins - continued cleanup and recovery efforts Tuesday.
French President Francois Hollande has said that the government would declare a state of emergency for the area and would unblock funds to help with the recovery.