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 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.
Other news from France:
- A 74-year-old man on horseback drowned trying to cross a flooded field south of Paris. The horse survived with minor injuries, local authorities said
- Fire services found the body of an 86-year-old woman in her home in Souppes-sur-Loing
- The French Open tennis tournament could be extended into a third week
- Floods also cut off the getaway of two suspected robbers in the town of Fleury-les-Aubrais. They fled their car and tried to make a swim for it, but were arrested
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.
Elsewhere in Germany:
- An emergency was declared in the historic town of Passau
- In Pfarrkirchen, more than 35mm of rain fell in the space of six hours on Wednesday
- In the district of Wesel, North Rhine-Westphalia, a dam is threatening to break
Belgium has also seen heavy rainfall and has reported flooding in many areas, including around Antwerp, Limburg and Liege.