France has shut down the equivalent of four nuclear power stations as the heatwave eats into the country's electricity generating capacities.
With temperatures in French rivers hitting record highs, some power plants relying on river water to cool their reactors have been forced to scale back production.
The French nuclear safety authority has given others permission to return the river water at a higher temperature than is normally allowed.
The precise consequences of higher river temperatures are not known, but it is thought that they could endanger fish. French meteorologists are calling this summer the country's hottest since 1947.
The chief executive of state-owned Electricité de France did not rule out further cuts, but said that the company would do all it could to maintain supplies.
"These past few days, we have shut 4,000mW of production capacity, which is the equivalent of four nuclear plants," Francois Roussely told France Inter radio.
He said that blackouts were not expected this week, but did not rule out the possibility of them happening if summer temperatures did not fall soon.
"We'll watch developments from here with weather forecasters," Mr Roussely told the radio station.
Around 80% of France's electricity needs are met by the country's 19 nuclear power stations, which have a total capacity of 62,520mW.
Although domestic supply has not yet been affected, France's net exports to the rest of Europe today fell by more than half.
During the hottest part of the day, between 8am and 8pm, France was expected to send about 4,000mW to Switzerland, Britain, Italy, Belgium, and Spain instead of the more usual 8,000 to 10,000mW, the French national grid said on its website.
A spokesman for the UK national grid said that Britain's electricity supplies, which can be boosted by 2000mW through a cross-Channel cable, would not be damaged by France's problems.
Prices for traded electricity fell today trading after hitting record highs at one stage yesterday, reflecting the belief that the steps taken in France and in Germany, plus a promise of cooler days, would ease demand.