Météo France warned of the danger of floods in 30 of France's 101 départements.
Normandy and much of the Paris region are affected, as are the mountainous regions of the Jura and the Alps and the Vosges, Meuse and Meurthe-et-Moselle in the east.
The Dordogne and Gironde in the south-west were also under threat.
Floods are possible in areas that not usually hit by them, the forecasters warn, and they advise people in relevant areas to avoid unnecessary journey and take precautions in properties that could find themselves under water.
Heavy rain lashed much of the country on Monday afternoon, although it eased up in Paris on Tuesday morning.
In the capital, the Seine reached 4.57 metres, flooding the riverside quays.
The flood-warning authority on Tuesday predicted that the waters will be as high as 6.10 metres, the level they reached in 2016, on Friday.
The local rail line RER C, which runs close to the Seine, has been ordered to close from Wednesday.
In the Alps melting snow added to the danger, leading to some ski slopes being closed.
In Normandy several roads were closed, the town-centre of Pont-L'Evêque was flooded and about 50 residents were evacuated in La-Rivière-Saint-Sauveur.