The Météo France weather service warned that floods are likely in the north-west of the country, but lifted an alert in four other western départements.
Part of the town centre of the seaside town of Granville were flooded Sunday morning, with water entering houses and shops, after 48.4 mm of water fell on the region in 24 hours.
Over the border in Belgium two people died overnight due to heavy rain and another died on Sunday afternoon.
One, a 72-year-old woman, was unable to get out of a car which was trapped by the water in the village of Solre-Saint-Géry, near the French frontier.
The body of a man was found in the same village. He had apparently been carried away by the torrent.
On Sunday afternoon another body was fished from the waters in nearby Lessines, where another person was reported missing.
In a week of storms in the north and east of France one person has died and another gone missing.