Up to seven months of rain fell overnight, turning the streets of the southern region of Aude into gushing rivers, local authorities said.
Television pictures showed raging, muddy rivers that had uprooted trees, knocked over concrete electricity towers and swept away cars.
National emergency services spokesman Michael Bernier said 13 people had been killed and one person was still missing, while thousands were being evacuated from the area.
A spokesman for the Interior Ministry said there is a chance of the death toll rising.
The worst hit regions of Aude, a region near the medieval hilltop city of Carcassonne, are villages of Conques-Sur-Orbiel and Villardonnel.
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Water has been reported as high as the first-floor windows of some homes.
Seven helicopters were scrambled to rescue people from the roofs of their homes, and rough weather was making operations difficult.
The prefect of Aude, Alain Thirion, said: “We have people stranded on rooftops.”
He continued: “We’re going to have to use aircraft to evacuate them because we cannot reach them by boat given the force of the water. It’s too dangerous”
Prime Minister Edouard Philippe said 350 firemen were helping the rescue effort and up to 350 more would be drafted in.
He will be heading to the disaster zone on Monday.
Water levels were expected to keep rising and schools were shut and residents told to stay at home.
“We’re being kept informed of the situation hour by hour,” he said.
The catastrophic flooding struck without warning.
At least one victim was swept away by raging waters while sleeping, Mr Thirion said.
The Vigicrues agency, which tracks water levels in France, said the flooding was nearing a peak last seen in 1891.
Torrential rain is not uncommon in France at this time of year.
However, meteorologists have said exceptionally warm sea water along the Mediterranean coast may be intensifying the rains.
The year so far is France’s hottest since 1900, according to the state meteorological service.
The Aude region is a popular tourist destination with ancient towns and villages in its hilly peaks stretching down to the Mediterranean.