She was launched in 1785 at Rochefort. With the Guillaume Tell, she was one of only two ships to escape the British attack at the Battle of the Nile in August 1798.
Shortly after the battle of the Nile, on 18 August, 1798, she fell in with a smaller British ship of the line, HMS Leander of 50 guns. After a long battle, the Généreux captured the Leander, with the Leander suffering 23 killed and 58 wounded and the Généreux suffered around 100 killed and 180 wounded.
She was captured by the Royal Navy in February 1800; Rear-Admiral Jean-Baptiste Perrée, the commander-in-chief of the French navy in the Mediterranean was aboard, and was killed at the start of the action. She became HMS Généreux and was finally broken up in 1816.