Weather bureau Météo France predicts snow storms will continue over Corsica until Thursday.
It warns of a high risk of avalanches in the island's mountainous regions.
3,000 Corsican households remain without electricity as engineers struggle to reconnect power lines. 10,000 homes were cut off in Monday's storms.
On the mainland, more than 6,000 motorists were left stranded after heavy snow blocked roads in the southern Aude and Pyrénées-Orientales departments. Local authorities opened community centres and school halls to provide travellers with shelter overnight.
A further 1,800 travellers slept aboard trains in Aude, while around 100 passengers were trapped on the Barcelona to Paris service in Pyrénées-Orientales.
Road and rail traffic resumed throughout Tuesday but remained congested. Authorities are advising people to avoid unnecessary trips, and take extra care if they do decide to travel.
At least one man, a 74-year-old from Port-Vendres on France's Mediterranean coast, is believed to have died as a result of the exceptionally icy weather. He was found in his garden on Tuesday morning.
Winemakers are concerned that their crops will also be casualties of the cold snap. Vines in the Perpignan region, known for its sweet white wine, were entirely covered in some case by up to 60 centimetres of snow.
The freak snow storm also caused havoc in other countries across Europe.
Spain saw its heaviest snowfall in 25 years, with up to 90 centimetres in mountainous areas. Some 40 roads were closed in Catalonia, next to the French border, where some 3,000 travellers were forced to find emergency shelter overnight. 200,000 households remain without power in the region, while schools were closed for 165,000 pupils.
In Bulgaria, at least four towns in the south and east have declared a state of emergency after snow cut off their lines of transport. Large eastbound sections of major motorways are also closed.
There was surprise snowfall in Italy, where the cities of Florenca, Sienna, Tuscany and Pisa and even the island of Elba found themselves covered. Public safety officials met rescue workers, police and officials from rail and motorway companies to prepare for more icy weather that is expected to hit on Wednesday.