The 22 crew of the Modern Express were evacuated by helicopter in dramatic scenes on Tuesday, but their ship remains under close observation.
The 164-metre-long vessel, which was carrying diggers and 3,600 tonnes of timber, gave out a distress call on Tuesday when it was situated 270 kilometres from the northwest tip of Spain, but it is still not known why it ran into difficulty.
The ship does not appear to be taking on water for now, authorities said.
It is drifting eastwards at a speed of 1.3 knots (2.4 kilometres per hour or 1.5 miles per hour).
A French frigate and a tug are at the scene and have been joined by two Spanish tugs sent by the ship's owners after French authorities warned them to take action to prevent the ship posing a danger.
Salvage experts are also in the area and will need to board the ship, but a swell of four metres made it impossible "to safely transfer on board the team required to prepare for a possible towing", the maritime authorities said in a statement.