The national weather agency Meteo France said winds powering to 160 kilometres (100 miles) per hour battered the Breton peninsula and Normandy coast overnight, and two other regions remained under a storm alert.
Enedis said 33,000 homes were without power in Normandy, 18,700 in Brittany and 16,500 in the Loire-Atlantique region, which lies south of Brittany.
A woman was seriously hurt in Brittany's Cote d'Armor department when her car hit a fallen tree, local officials said.
The fire brigade in Brittany was called out more than 600 times during the night, mainly to clear blocked roads, they said.
Meteo-France said storm conditions in the northeastern Atlantic had combined with a strong airstream directed at northwestern France, producing "an event that occurs three or four times per year."
The agency maintained a high-winds alert for three departments -- the rough equivalents of counties -- in the northwest, and for three in the centre-east. The winds were expected to die down on Monday.