Communications with the naval boat were lost after it was hit by high tides.
The search was conducted near the border between Maltese and Libyan territorial waters.
The Maltese military said in a statement that the bodies had been found in Libyan waters.
The statement said “diplomatic efforts are currently under way between France and Libya” for the French frigate to enter port and offload the corpses.
Several boats carrying illegal migrants have recently sunk in the same area.
Last week 27 shipwrecked Africans spent three days clinging to tuna nets in the Mediterranean while Malta and Libya argued over who should rescue them. They were eventually picked up by the Italian navy.
On May 21, a boat carrying 53 migrants disappeared near Malta after being spotted by a Maltese military aircraft. Rescuers sent to the area could not locate the boat.
A few days later, a vessel that had left from northern Africa sank off Maltese coast.
The sole survivor, a 23-year-old man, said 28 other people had been aboard.
Every year thousands of immigrants attempt to make it to Europe across the Mediterranean from northern Africa, often undertaking dangerous journeys in unsuitable craft.