Much of eastern France was on orange alert for winds of up 130km per hour Friday, while the north, especially Normandy and the Ardennes, was on alert for five to 10 centimetres of snow and ice.
The weather was expected to improve in the afternoon.
The main areas affected by Thursday's power cuts were in Normandy but electricity was down as far across the country as the eastern Champagne-Ardennes region.
Emergency services were called out 4,452 times and about 1,000 people were moved out of their houses.
Passengers spend night on train
Some 180 people were stuck on a Brussels-Paris train from 3.00am to 7.45am near Albert in the Somme, services were cut on the Rouen-Le Havre and Rouen-Dieppe lines from 8.00pm Thursday evening and disrupted in the Paris region.
About 50 people were slightly injured, one hit by a falling tree in the Oise region north-west of Paris.
Train services and flights from northern regional airports were disrupted.