The sheet of oil, 10 kilometres (six miles) long and one km wide, could hit parts of the country's southwest region near the port city of Bordeaux this weekend.
"According to our forecasts, fragments could reach some areas of the coast in Nouvelle-Aquitaine by Sunday or Monday owing to bad weather, which also risks making the anti-pollution operation more difficult," environment minister Francois de Rugy said Wednesday.
France will deploy four ships to help battle the oil slick at sea and will prepare for a clean-up operation on land, he added.
The Grande America was en route from Hamburg in Germany to Casablanca in Morocco when a fire broke out late on Sunday.
All 27 people on board were evacuated the following day as the fire worsened, before the ship sank some 300 km west of the town of La Rochelle on Tuesday.
"For now the possible pollution risk consists mainly of the 2,200 tonnes of heavy fuel oil on board," Jean-Louis Lozier, head of the regional maritime authority, told reporters in Brest on France's Brittany coast.
Lozier said the hybrid ship's Italian owner Grimaldi had indicated that 365 shipping containers were onboard, "of which 45 are carrying dangerous materials", as well as around 2,000 vehicles.