Floodwaters in Paris are forecast to peak on Friday with the River Seine due to reach 6m (19ft) above its normal level.
The world-famous Louvre and Orsay museums have been shut so staff can move priceless artworks to safety.
Flooding across France and Germany has left at least 11 people dead and forced thousands from their homes.
More downpours are forecast through the weekend across a band of central Europe from France to Ukraine
As much as 50mm (2in) of rain is expected to fall in some regions in just a few hours.
Several towns in southern Germany have been devastated and Belgium and Poland have also been affected.
French President Francois Hollande said the weather was a serious climate phenomenon and a global challenge.
He is to declare a state of natural disaster in the worst-hit areas, which will free up emergency funds.
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 devast
At least nine people have died in recent days in Germany, while several people are missing.
Chancellor Angela Merkel said the country was in mourning for those who had lost their lives.
The worst incident was in Simbach am Inn in Bavaria, southern Germany, where a woman, 78, her daughter, 56, and granddaughter, 28, were all found drowned in the basement of their house.
Another woman, aged 80, was found dead in the nearby village of Julbach, while a 75-year-old man was the latest to be found dead, in Simbach.
Earlier in the week, four people died in floods in south-western Germany.