The French Navy's anti-submarine frigate, Jean de Vienne, the Indian Navy's destroyer, INS Mumbai, and frigate INS Trikand are among the vessels participating in the exercise.
The Indian Navy's submarine, Kalvari, P8-1 and Dornier maritime patrol aircraft and MiG 29K fighter aircraft are also participating. The first phase of the exercise will end on March 24, a defence official said.
The second phase will be held off the Chennai coast in April and the third near La Reunion Island in May.
India and France will explore measures to facilitate operational-level interactions between their armed forces and increase mutual cooperation, considering the common global threats, the official added.
Rear Admiral MA Hampiholi, Flag Officer Commander, Western Fleet of the Indian Navy, said "Varuna-18" would be conducted in three sea areas, including the Arabian Sea, Bay of Bengal and South Western Indian Ocean.
Real Admiral Didier Piaton, who is heading the French side for the exercise, said India was a major partner of France in the Indian Ocean region. "Maritime security is a priority in our defence and security policy, along with the fight against terrorism," he added.
The Indian Navy and the French Navy have been conducting naval exercises since 1983. These exercises were christened as "Varuna" in 2001. The last edition of the exercise was conducted off the French coast in April last year.
The "Varuna" series of exercises has grown in scope and complexity over the years and provided an opportunity to the naval forces of both countries to increase interoperability and learn from each other's best practices, the official said.