The River Seine has raised 20ft (6m) above its normal level as record floodwaters hit the French capital.
The world-famous Louvre and Orsay museums have been shut so staff can move priceless artworks to safety.
The number of dead in the floods has now risen to at least 14 – 10 in southern Germany and two each in France and Romania.
More downpours are forecast for the weekend across a band of central Europe from France to Ukraine.
Several towns in southern Germany have been devastated. Belgium, Austria, the Netherlands and Poland have also been affected.
Thousands of people have been forced from their homes.
France’s President Francois Hollande said the weather was a serious climate phenomenon and a global challenge.
Francois Hollande 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, a number of bridges have been closed and tourists boats have been banned from sailing on the river.
The Seine has not reached present levels in Paris since 1982, according to the environment ministry.
The river previously reached 6.18m in 1982, 7.1m in 1955 and 8.62m in 1910.
Rail operator SNCF has closed a line that runs alongside the Seine in central Paris.
More than 5,000 people have been evacuated from towns in central France since the weekend and 19,000 homes are without power, the AFP news agency reports.
The French Open tennis tournament, meanwhile, could be forced to extend into a third week.