It comes weeks after Turkish ships allegedly targeted a French warship in the Mediterranean – something Ankara strongly denies.
The Nato allies are thought to support different sides in Libya’s civil war.
Riven by violence since Col Muammar Gaddafi was deposed by Nato-backed forces in 2011, the oil-rich nation is a key transit point for migrants heading to Europe from Africa.
Currently, the UN-backed Government of National Accord (GNA) is battling against the forces of Gen Khalifa Haftar which control large parts of the east and south of Libya.
Why is France pulling out of the operation?
French relations with Turkey have become increasingly strained in recent months because of the Libya crisis, Turkey’s role in northern Syria, and also drilling in the eastern Mediterranean.
But the key incident came on 10 June, when French frigate Courbet went to inspect a Tanzanian-flagged cargo ship, Cirkin, off the coast of Libya, to check if it was smuggling arms.