The 20 minute "deluge" hit villages in the east of the Somme département, not far from the border with Belgium, late on Tuesday, local government chief Stephane Haussoulier told AFP.
The storm triggered large mudslides in some places and set loose a "river of mud" in the worst-hit village of Sailly-Laurette, he added.
Sixteen vehicles were swept away at Sailly-Laurette, which is on the banks of the River Somme. Eleven homes were flooded, some roads destroyed and 24 people evacuated, Haussoulier said.
Locals were out Wednesday clearing a thick layer of mud from streets and gardens, an AFP journalist saw.
At least 10 more villages in the eastern Somme were affected by mudslides.
Videos posted to social media showed flows of mud oozing through the streets of several municipalities.
In some places, it completely covered the wheels of cars struggling to make headway.
The flooding "caused material damage to around 100 homes", the Somme departement's préfecture said in a statement.
It added that firefighters had responded to 83 calls.
Earlier this month, a 57-year-old woman was killed in a mudslide in Courmelles, around 100 kilometres south of Sailly-Laurette.
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