France has declared a state of natural disaster for the hardest-hit areas, allowing the release of emergency funds to local authorities. In neighboring Germany, residents battle against further damage from flash floods.
The wave of water has killed 11 people as of Friday -- 10 of them in southern Germany and one on the outskirts of Paris -- and has caused chaos in the French capital, which shut down several busy train lines and part of its metro, adding to the congestion on its roads.
The French army has assisted in rescue operations after days of heavy rains crippled the city.
A 74-year-old man riding a horse on the southeastern outskirts of Paris was swept away, CNN affiliate BFMTV said.
State of natural disaster
In France, the Seine is expect to burst its banks by Friday evening. The river level is fast approaching 6.5 meters (21.3 feet), the highest in more than 30 years, according to the environment ministry. It could take weeks for the river to be back in normal limits.
All train lines running next to the river's banks will be closed and the bank will be completely off limits, French weather service Météo Villes warns. Some pedestrians managed to snap photos of the rising river water.
People living in houseboats told CNN they had seen debris rush by their homes, including building parts, trees and a refrigerator.
The floods have only exacerbated France's troubles as it tries to keep gas stations from running dry, cities powered and workers on the move amid nationwide workers' strikes that have gone on for two weeks, immobilizing some essential services.
The Interior Ministry announced that nearly 20,000 people have been evacuated.
'Mona Lisa' stays dry
The Louvre is carrying out the daunting task of moving 150,000 pieces of art -- mostly ancient Islamic, Greek and Italian artifacts -- from its lower floors as floods threaten to creep into the busy tourist site. Around 7,000 of these items had been on display until Thursday; the remainder were being kept in storage.
CNN was given access to the Louvre as its staff set out on the massive rescue operation, watching as Italian vases from the 7th century B.C. were carefully wrapped and packed into gray crates -- the process painstakingly documented to ensure nothing is damaged or goes missing.
"Due to the level of the river Seine, the Musée du Louvre will be exceptionally closed to the public on June 3, 2016 to ensure the protection of the works located in flood zones. We apologize for any inconvenience caused," the museum said on its website.
The "Mona Lisa" will stay dry on her upper floor in the Louvre.
The emergency plan is expected to take 72 hours to carry out.
The Musée d'Orsay, which houses a rich collection of Impressionist paintings, including some by Van Gogh, Cézanne and Manet, followed suit Friday, shutting its doors for the day.
'Like Noah's Ark'
American journalist Mort Rosenblum, author of "The Secret Life of the Seine River," has lived by the river for 30 years. He has never seen the river level this high.
"This is June; one night we're sitting on the deck having wine and it's perfectly normal, expecting the little ducks to float by in the morning, you know, calmly, and the next morning you wake up and it's like Noah's Ark," he told CNN.
Officials are hoping they can mop up the mess before next week, when the Euro 2016 soccer championships kick off. The monthlong event is expected to attract some 2.5 million people.
In Germany, parts of Bavaria have been profoundly affected, with some houses completely inundated and cars abandoned in the deluge.
A radio station posted a picture of refugees, ankle deep in mud, helping the local community in the town of Simbach repair damage to buildings.
But many in France managed to find some humor in the situation. One Twitter user posted a mock Uber map, implying that the car hire service would need to provide boats to serve its customers around the Seine.
Another tweet showed a doctored picture of a Paris metro train, complete with paddles.