PARIS — Muddy rivers and streams swollen by torrential rains tore through southwestern France on Monday, swamping towns, cutting off roads and killing at least 11 people, according to French officials.

Most of the flooding occurred in the Aude region, named after the river that runs through it, after several months’ worth of rain fell within hours overnight — nearly 14 inches in some places, according to the Interior Ministry.

In Trèbes, near the city of Carcassonne, the official agency that tracks flooding nationwide described the rise in the water level — over 20 feet — as “exceptional,” and said it had nearly reached the record set in 1891. At least six people were killed there, the Interior Ministry said.