A Con-Ro vessel operated by Grimaldi Lines caught fire in the Bay of Biscay on the night of Sunday, March 10.
Grande America was en route from Hamburg to Casablanca when a fire broke out on board just after 23:00 local time while the ship was 263 kilometres southwest of Brittany. The crew failed in their efforts to contain the blaze, forcing them to issue a distress call.
The spread of the fire eventually forced the crew to abandon ship at around 02:00 on March 11.
The Royal Navy Type 23 frigate HMS Argyll was sailing home to Plymouth after a nine-month deployment in the Asia-Pacific region when it responded to the mayday call from Grande America.
The frigate then proceeded to the area of the incident and managed to pick up all of the Con-Ro ship's 27 crewmembers out of the water.
The rescue lasted eight hours due to the difficult sea conditions, the Royal Navy said in a statement.
All of the rescued crewmembers suffered smoke inhalation but sustained no life-threatening injuries.
Argyll later turned over the rescued crewmembers to French authorities for medical treatment in the port of Brest as the fire continued to rage aboard the vessel.
The French Navy has deployed the FREMM frigate Aquitaine, a fixed-wing surveillance aircraft, and a helicopter to monitor the situation and check for any signs of pollution as the stricken vessel was in France's exclusive economic zone (EEZ) at the time of the incident.
A civilian tug has also been sent to the area.