Power was restored to most affected homes on Wednesday morning but during the night much of Brittany and the western coast had been without electricity.
As the Bretons got their power back, the lights went out further east, in Honfleur on the Normandy coast.
The cause was the sudden rise in temperatures, although the area concerned was far from the hottest part of the country, according to electricity provider RTE.
Devices measuring power in electriticy lines were overwhelmed and overheated, causing fires to break out in some places, although firefighters soon put those out.
Forty-seven departments were placed on orange alert on Wednesday with temperatures reaching 40°C in the Bordeaux area and forecast to go that high in Champagne, Burgundy and Périgord, in the south-west.
The lack of cooling breezes was expected to lead to pollution in Paris, where temperatures were in the high 30s.
Temperatures were as high, if not higher, than in 2003, when old people, especially, suffered and some 19,000 people died due to the heat.
This time the authorities are better prepared and Health Minister Marisol Touraine on Wednesday said that health services are coping well.
But she reminded people that they should be drinking water and staying in cool rooms and called on neighbours to keep an eye on vulnerable people.
The heatwave hit most of western Europe this week with temperatures soaring in Portugal, Spain, Britain, northern Italy, Belgium and The Netherlands.