The nuclear power producer EDF is reducing output because the heatwave has meant rising river temperatures limit its ability to use water to cool the plants.
The French state-backed energy company said output at plants on the Rhone and Garonne rivers have been affected and that more cuts were possible at other plants.
The company told The Times that it was lowering production for a few hours at a time and that no nuclear plants would be shut. But the reductions were putting further pressure on power prices, which are already at record levels in France.
Reactors at St Alban, Bugey and Tricastin on the Rhone, and Blayais on the Garonne, have already been affected. These, and another site at Golfech, 55 miles north of Toulouse on the Garonne, face further cuts, possibly this week.
Temperatures in parts of France are forecast to reach 40C, and are expected to remain above average for about two weeks.
During a heatwave in 2003, the country’s nuclear safety authority imposed restrictions to ensure that the water-cooling systems of the plants would not damage wildlife when circulated back into the rivers.
Europe is suffering its worst energy crisis in decades after reductions in exports from Russia after it invaded Ukraine.
In Germany, Bloomberg reported, the Rhine is on the brink of having to close to commercial traffic at a key waypoint because it has become too shallow for barges carrying coal to pass. Navigation has also become harder on the Danube, while in Italy levels of the Po, the country’s longest river, are too low to water farm fields.
EDF has estimated that output this year will be at the lowest rate in three decades because several plants are shut for maintenance and checks. Because of that France, traditionally a power exporter, has had to rely on imports from neighbours, such as Britain, which are facing their own energy crisis.
Last week, EDF posted its fourth profit warning this year when it reported a loss of €5 billion.
The French government, which owns 84 per cent of EDF, has unveiled plans to take full control.