A 35-year-old homeless man was found dead by his companions in the south-eastern city of Valence on Sunday and on Friday the body of a 62-year-old who lived in a cabin in the woods near Paris was also found.
Both probably died because of the cold, officials said.
Weather forecasters show tempatures plummeting
As temperatures drop to as low as -10°C in the east of the country, the authorities have ordered 3,100 emergency accommodation places to be opened, 500 of them in Paris.
Police in Paris report that most homeless people have gone to shelters, apart from migrants, many of whom are unaware of the arrangements or may fear deportation.
The cold front has been dubbed "Moscow-Paris", coming as it does from Russia, where the thermometer was expected to fall to -35°C in the centre of the country.
North-east winds of 60-70km/h will bring a wind-chill factor that will make -10°C feel like -16°C.
Tuesday and Wednesday are expected be the coldest days but the snow may head north, possibly as far as Paris and the Channel coast, on Thursday and Friday.
Health Ministry advises French to wrap up warm
[#GrandFroid❄️] Ces prochains jours, les températures vont baisser, partout en France.MinSolidaritésSanté (@MinSoliSante) 24 février 2018
⚠️ Le Ministère de l’intérieur (@Place_Beauvau ) vous invite à limiter vos déplacements
Les conseils santé pour se protéger du #froid ⬇️ pic.twitter.com/7ynkcUhokm
The authorities warned old people to stay indoors and parents to keep babies at home.
They also advised the rest of the population to wrap up warm and limit physical activity to avoid the danger of frostbite, hypothermia and heart attack and called for restraint in electricity consumption, pointing out that power supply produces the most carbon emissions during cold snaps.
Interior Minstry appeals to French to limit electricity use
Temperatures at the end of February have not been so low since 2005.
The exceptional weather comes after a changeable winter that saw an unusually mild January followed by snow in February.
Snow and ice may disrupt traffic on some motorways, operator Vinci Autoroutes warned.
Power supply company RTE said it was not anticipating major problems.