Three others were rescued after the Maritime and Coastguard Agency (MCA) was alerted that the vessel, with five people on board, was “in distress” off the coast of Plymouth, Devon, just after 6pm on Saturday.
The vessel was believed to have been in trouble southwest of Eddystone Lighthouse, which is 15 miles south of Plymouth.
The MCA said a rescue operation was launched, with a coastguard helicopter, a fixed-wing aircraft, and RNLI lifeboats from Falmouth and Plymouth scrambled to the area.
The French Navy’s Falcon 50 was also deployed to assist.
Those rescued were taken to hospital, but the agency said on Sunday night that the search for the two remaining crew members had been “suspended pending further information”.
In an earlier statement, the coastguard said: “Three people were rescued last evening from the French-registered fishing vessel which had made the call for help. They were taken to hospital for further care.”
The statement added: “The vessel has sunk.”
