Police and municipal employees have stepped up patrols of areas where the homeless are known to gather, notably public parks and allotments, to try to persuade them to head to special hostels.
Ukraine reported 27 deaths, while six people were killed in accidents in Germany and three in Austria.
In France, the electricity grid was forced to cut off power to around two million people in the southeast in order to avoid a massive regional blackout, the operator said.
"RTE has put in place a programme of controlled load-shedding in order to avoid a complete black-out in the region," an RTE spokesman said, referring to the Provence Alpes Cote d'Azur region.
Some districts of Marseille, including the city centre, and the suburbs of Nice, were without power in the afternoon.
The country was forced to import power earlier than normal this winter and has warned that cold weather could force cuts because of near record consumption and delays to maintenance in its network of nuclear power stations.
At least two homeless people were reported to have died as the temperatures fell.
Flights were cancelled in France, Germany, the Netherlands, Portugal and Spain and main highways were blocked across Europe where some regions had more than 50cm of snow.
About 700 people spent the night on camp beds at Amsterdam-Schipol airport and more flights were cancelled after dozens were grounded on Sunday.
At Frankfurt and Duesseldorf airports in Germany more than 500 flights were cancelled or redirected.
And at Paris-Charles de Gaulle airport, 20 per cent of outbound flights were cancelled.
Eurostar services - which take rail passengers between London and Paris - were cancelled for a third consecutive day because of technical problems caused by the low temperatures.
The traffic disruptions have left thousands of passengers wondering how they will complete their journeys before the Christmas holidays.