Water levels are around four metres above normal for the time of year, the BBC reports, with an estimated 1,500 people evacuated from their homes.
Seven Metro stations and some stretches of road beside the river are also closed.
The Bateaux Mouches tourist boats are not running, with only emergency services allowed to use the river. The flood has closed a lower level part of the Louvre museum, but waters are expected to start receding on Tuesday.