Seven departments, or counties, in Normandy and Brittany were placed on "orange" alert, the second highest in Meteo- France's three-stage warning system.
At least 60,000 homes were without power, more than half of them in the French western peninsula of Brittany, electricity grid operator ERDF said.
Firemen across the two regions were called out more than 400 times, mainly to clear roads blocked by fallen trees and debris, emergency services said.
Coastal dwellers in three departments on the Atlantic -- Finistere, Morbibhan and Loire-Atlantique -- were warned of storm-surge waves.
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In Britain, the same weather system -- dubbed "Storm Katie" -- left a trail of disruption in its wake as it swept across southern England overnight, leaving debris and roadwork barriers strewn across London's streets.
Winds gusting to 170 kph an hour forced the cancellation of around 150 flights in and out of Britain and left around 2,000 homes without power.
Heathrow, one of the world's busiest airports, reported around 130 cancellations with other flights delayed or diverted to other airports.
The Met Office national weather service issued an amber warning for winds for London and southeast England, advising people to be "prepared for disruption to outdoor activities and travel".
The service recorded gusts of 170 kph off the southern England coast, with winds of over 112 kph registered across the south.
A bridge crossing the River Thames in southeast England and the Severn Bridge which connects England and Wales were also closed, according to Highways England.
UK Power Networks said they were dealing with problems across Sussex, Surrey and Kent in southern England, leaving at least 2,000 households without electricity.
Weather forecasters in both countries expected the storm to fade by the afternoon.