The cold weather, which is creating chaos across the continent, is believed to have led to over 300 deaths in the last week around Europe.
A 12-year-old boy died on Saturday when he fell into an icy lake in the eastern Vosges area. The boy was walking with his 11-year-old brother when the accident occurred.
A 56-year-old homeless man froze to death in a tower block on Saturday in a suburb east of Paris. Another homeless man aged 46 was also found dead on Saturday in a squat in the north-east town of Compiègne.
On Friday, two old people suffering from Alzheimers were found dead after they had ventured out without adequate protection.
A surge in electricity demand on Monday evening due to the freezing weather will put strains on the national supply as power demands push the country towards its maximum capacity.
"We are likely to reach a new record for electricity demand on Monday evening," said Henri Proglio, head of national electricity company EDF.
The Var and Alpes-Maritime regions in the south of the country were at greatest risk of having power cuts, reported BFM TV on Monday morning.
The two departments include the towns of Cannes, Nice, Toulon and Saint-Tropez.
EDF said the region, along with the north-east Brittany area, were both at the extremes of the country's power grid and had "neither the means of production nor sufficient transport" for the power they might need.
Residents in those areas were being asked to moderate their consumption on Monday evening between 6 and 8pm.
Freezing conditions are expected to continue until at least Wednesday with half the country placed under "orange alert" by the national weather forecaster, Météo France.
An orange alert warns of "dangerous" conditions with special attention needed on roads.