The helicopter, an AS 532 Cougar, had 10 troops on board, including six special forces paratroopers.
It fell into the sea shortly after take-off from the French carrier La Foudre.
Three soldiers were rescued on Saturday but one later died in a hospital in Libreville, the Gabon capital, the French army said.
The reasons for the accident were not known. A judicial and a French defence ministry investigation will take place, according to the defence ministry.
There are about 1,000 French troops in the west African nation, a former colony which holds one of France's four permanent military bases on the continent.