An oil slick was reported to be floating toward the coast between the city of Lorient and the Quiberon peninsula, according to the Brest maritime authorities.
Regional authorities were preparing to deploy equipment to try and contain the slick and to empty the ship of its 180 tons of fuel and 40 tons of diesel, it said.
All 19 members of the ship's crew, which was flying the Maltese flag, were evacuated by helicopter, it said.
The storm has been battering the region of Brittany since Thursday night, with gusts of wind of up to 133 kilometres (83 miles) per hour and waves up to seven metres (yards) high.
The storm has left nearly 200,000 households without electricity and wreacked havoc on train traffic in Brittany and the Pays de la Loire region due to debris falling on tracks, according to regional authorities and the SNCF rail operator.