Electricity distributor ERDF said half of the homes were in the Finistère department, the region worst hit by the storms.
Three departments – Finistère, Côtes d’Armor and Morbihan – were placed on “Orange Alert”, the second-highest level of weather warning.
Emergency crews attended to more than 500 calls for help in Finistère, mostly for fallen trees.
Trains have been cancelled between Rennes and Brest, affecting around 2,000 passengers, according to rail company SNCF. Flights have also been cancelled at airports in Brest, Lorient and Quimper.
Météo France said wind gusts reached 150 kilometres an hour between Friday night and Saturday morning.
The storm also dumped heavy rain across the region. Authorities in the town of Quimperlé in Finistère said riverbanks overflowed by 40 cm.
In Brest, 636mm of rain has fallen since mid December.