At least 13 people have died after violent rainstorms turned rivers into raging torrents in south-west France, in the latest episode of wild weather in Europe, officials have said.

Flash floods swamped a number of towns and villages around Carcassonne, leaving a trail of overturned cars, damaged roads and collapsed homes.

A nun was swept to her death as rising waters destroyed a nunnery in the village of Villardonnel. At least four people died overnight in the village of Villegailhenc, local authorities said on Monday.

As Édouard Philippe, the prime minister, headed to the scene, the French interior ministry said 13 people had died after the equivalent of three months’ rainfall in a few hours.

Helene Segura, a resident of Villegailhenc, where at least one small bridge collapsed, said: “There’s water everywhere in the house. Everything is flooded.

“When I look out the window, I can only see water and mud everywhere. It’s sad when you’re 70 years old like me and you need to redo your house, change the furniture and all the upholstery.”

Authorities rushed in helicopters and 600 firefighters to help with rescue operations, particularly in the floodplain of the Aude River, which reached its highest level in 100 years, according to the Vigicrues flood agency.

In the town of Trebes, the river’s level rose eight metres (26ft) in five hours, officials said.

About 1,000 people were evacuated in Pezens due to fears a nearby dam could burst.

The storms were triggered when a front of warm and humid air from the Mediterranean collided with colder air around the Massif Central, inundating an area from the eastern Pyrenees to Aveyron further north.

Elsewhere, 28 people were left with minor injuries and hundreds of thousands without power as violent storms hit Portugal on Sunday, resulting in flooding in the region around Lisbon.

The heavy rain, which later passed over Spain, was the tail end of Hurricane Leslie in the Atlantic, which weakened to a post-tropical storm as it made landfall.

Last week, an unrelated weather system moving across the Mediterranean killed 12 people in Mallorca, and another two in south-east France.

In the latest incident, firefighters responded to more than 250 calls overnight, as between 160mm and 180mm (6-7in) of rain fell within five hours in Carcassonne.