Before 9pm on Saturday more than 95% of affected households had their electricity supplies restored. Efforts to reconnect the remaining few to the grid will be carried throughout Sunday.
Earlier attempts to restore electricity supplies were hampered by heavy snowfall.
On Friday, some 12,000 households experienced electricity shortages.
France’s national meteorological service put the affected departments, Bas-Rhin and Haut-Rhin, under yellow alert.
The local prefecture had to close the ski area of Markstein in the Vosges, citing fallen trees and the increased risk of accidents.
Several local roads in Alsace remain closed. The disruption, however, is not expected to last beyond Sunday, a prefecture spokesperson said.
