A specialised Dutch company, Smit Salvage, started pumping the 70 tonnes of fuel oil out of the Luno after managing to get through the hull on Saturday morning.
The operation was supposed to start on Friday but was unable to go ahead because of difficulty of safe access to the tanks.
The ship's captain, Jean-Bernard Cerutti, said that the operation could be over by Saturday evening.
Another 20 tonnes, which had been in a tank in a different part of the boat, appear to have already leaked but officials say that nearby beaches will not be polluted.
There seem to be no grounds for legal action against the owner or crew, public prosecutor Anne Kayanakis said on Friday.
While parts of Brittany remained on flood alert, the towns of Morlaix and Châteaulain
, which were flooded during the week, are now in a much better condition, officials say, while Quimper seems set to improve but the situations is still "serious" at Quimperlé.
Some minor roads were impassable on Saturday and traffic was disrupted on the main road, the RN24, betweeen Rennes and Lorient.
The weather is expected to improve slightly on Sunday but there may be more floods in the middle of the weeks when new storms are forecast.
All weekend football matches in Brittany were cancelled due to the weather.