The planes are the Dassault Rafale - a twin-engine, canard delta wing, multirole fighter aircraft.
The induction ceremony was completed in the presence of French Defence Minister Florence Parly and her Indian counterpart Rajnath Singh.
It comes at a time of heightened military tension with India's neighbor, China.
India has received five Rafales of the expected 36 aircraft from France, in what was country's biggest defense deal worth $8.7 billion.
Indian Prime Minister Narendra Modi has vowed to modernize India's armed forces with a $150 billion spending spree.
The Indian Air Force has also recently inducted S-400 missile systems from Russia, and Apache helicopters from the United States.