The area includes 24 departments in northern and central France, and in the Paris area.
Meteo France has issued an orange alert — the second-highest warning level — for snow and ice.
In Paris, about five centimeters (two inches) of snow fell on Tuesday and the Eiffel Tower has been closed as a precautionary measure. A major road in the Paris region, where 2,000 drivers were trapped for a night in February last year, was closed to traffic in the morning. The road reopened in the afternoon, but truck traffic will be banned on the route from 9 p.m. (2000 GMT; 3 p.m. EST).
"The situation is under control," Transport Minister Elisabeth Borne said. "Drive safely and avoid hard braking."
The weather agency says the snow should last until Wednesday.