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Up to seven months' rain fell in just a few hours overnight, local officials said, catching sleeping residents by surprise and isolating villages.
Several deaths were in the town of Trebes, which sits between a canal and two rivers, including the Aude.
As the death toll rose and the extent of the damage became clear, President Emmanuel Macron decided to hold off on an already-delayed reshuffle of his cabinet.
"It's like a war zone. The village is more or less cut off from the outside world," said Jean-Jacques Garros, a resident of Villegailhenc, one of the hardest hit areas.
The Interior Ministry initially put the number of deaths at 13 before revising the toll downwards.
Prime Minister Edouard Philippe flew to the disaster zone to meet with emergency service personnel. Some 350 firefighters were involved in rescue operations, a number which will double as more are drafted in to deal with the aftermath.
Television pictures showed churning, muddy rivers that had uprooted trees, knocked over concrete power pylons and tore up roads in the southern region of Aude, near the medieval hilltop city of Carcassonne.
Nine helicopters were scrambled to rescue people from the roofs of their homes as rough weather complicated operations earlier in the day. Thousands of people have been evacuated from the area.
Among the worst hit were the villages of Conques-sur-Orbiel, Villegailhenc and Villardonnel, where the water rose as high as the first-floor windows of some houses. The Aude region is a popular tourist destination with old towns and villages in its hilly peaks and land stretching down to the Mediterranean.
The flash floods struck without warning. At least one victim was carried away by raging waters while sleeping, according to Alain Thirion, the prefect of Aude.
Schools were shut and residents told to stay at home.
The Vigicrues agency, which tracks water levels in France, said the flooding was nearing a peak last seen in 1891.
Torrential downpours are not uncommon in France at this time of year, but meteorologists have said that exceptionally warm sea water along the Mediterranean coast may have intensified the rains.
The year so far is France's warmest since 1900, according to the state meteorological service.