Floodwaters in Paris are forecast to peak on Friday with the river Seine due to reach 19 ft above its normal level, officials said.
The world-famous Louvre and Orsay museums have been shut so that staff can move priceless artwork to safety, BBC reported.
As much as 50 mm of rain is expected to fall in some regions in just a few hours, weather officials announced.
In Paris, emergency barriers have been put up along the Seine, which burst its banks in places.
Rail operator SNCF has closed a line that runs alongside the Seine in central Paris.
About 25,000 people are without power in Paris and central France.
In Nemours, 3,000 people have been evacuated from the town centre. The town’s Loing river, a tributary of the Seine, now has levels not seen since the devastating floods of 1910.
Six weeks’ worth of rain has fallen in three days in the Loiret department, submerging roads and forcing drivers to abandon their cars.
President Francois Hollande is set to declare a state of natural disaster in the worst-hit areas.
The downpours are forecast to continue through the weekend.