Earlier on Monday, some 40,000 households in the Brittany region experienced power cuts but 30,000 have now been reconnected said Enedis, which has mobilized 1,500 staff to restore fix power lines.
Enedis, a unit of French state-controlled utility EDF, said in a statement the storm was now moving to the regions of Poitou-Charente, Pays de Loire and Aquitaine.
Weather service Meteo France kept the French Atlantic coast areas south of Brittany on orange alert, but downgraded the threat level in most other areas of western France.
Winds with speeds of up to 140 kilometers per hour battered the country's Atlantic coast in mid-afternoon but no serious damage was reported.
Major power cuts or blackouts are rare in France, which produces three quarters of its power with nuclear energy.
In July 2015, some 830,000 households temporarily lost power in western France after exceptionally warm weather damaged transformers.