National weather forecaster Météo France has placed 28 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.
The Alsace, Lorraine and Franche-Comté regions in the east were all badly affected on Thursday as were the central Corrèze, Creuse and Cantal areas.
Even the Mediterranean port town of Marseille was affected, with palm trees covered in snow. Heavy goods vehicles were held back on motorways into the town causing traffic delays.
Météo France blamed the cold snap on a Siberian wind which made temperatures feel much colder than they really are.
Temperatures across the country were unlikely to get above between -3 and -6 degrees on Thursday, with the wind chill making the air feel much colder.
Newspaper France Soir reported that several regions were also at risk of losing electricity due to excessive demand. These included the north-west region of Brittany and the southern Alpes-Maritimes, Var and Monaco.
Residents of those areas were being asked to limit their electricity consumption between 6pm and 8pm.
The national electricity grid operator RTE (Réseau du Transport Electrique) predicted that national electricity consumption would reach a peak of 95,500 megawatts at 7pm on Thursday evening. This would take it close to the highest ever consumption figure of 96,710 megawatts on December 15th 2010.
Temperatures are expected to fall even lower over the next few days, with -10 degrees expected in central France and around Paris.