Three carriages were overturned on the RER B line between Saint-Rémy-lès-Chevreuse and Courcelle-sur-Yvette, south-west of Paris, Transport Minister Elisabeth Borne told Franceinfo radio.
Heavy rain caused an embankment to collapse just before 5.00am, leading the carriages to derail and tip over.
Three of the seven injured, one of them a pregnant woman, were taken to hospital, while the others were able to go home.
None of the injuries was serious.
Pregnant woman saved from flooded home
Most of the north of the country and some of the south-west was on orange storm alert on Tuesday, following a week in which four people died in weather-related accidents.
There were hundreds of emergency calls on Monday:
In the central Loiret region firefighters saved a pregnant woman who was washed out of her house when water smashed a bay window half of which was below ground level;
Fifty-three millimetres of rain were recorded in the western city of Nantes, with 33 millimetres in just one hour;
Melting snow added to rain led the Gave du Pau river to rise to within 25cm of overflowing in the Lourdes Catholic sanctuary and baths where pilgrims take the waters had to be closed;
There were several floods and mudslides in the eastern Ardennes region and pupils were trapped in a number of schools;
In the south-western Dordogne region the 10th-century Chancelade Abbey was under a metre of water.
"From Wednesday on it will be more or less the end of hostilities," apart from in the south-east, Météo France promises.