National weather forecaster Météo France placed twenty French departments on "orange alert", the second highest of the warnings it gives.
An orange alert warns of "dangerous" conditions with special attention needed on roads.
BFM TV reported on Tuesday morning that a triangle between the southern towns of Lyon, Valence and Saint-Etienne was particularly badly affected.
Roads in the Lyon region were causing some problems for Tuesday morning commuters. Heavy trucks were being banned on some roads in the area.
After a mild winter so far temperatures were back to more seasonal norms this week.
Snow is expected to keep falling until Tuesday evening, after which conditions should ease.