The defence minister sat in the rear cockpit of the customised Rafale fighter jet with tail number RB-001 and was flown by Philippe Duchateau, head test pilot of Dassault Aviation.
In a tweet, the IAF welcomed the "new bird" into its arsenal.
"The meeting demonstrated the depth of India-France bilateral partnership, especially in the defence sector, that has significantly strengthened in recent times. Both leaders resolved to take the relationship to the next higher level," said a statement issued by the ministry after the 35-minute meeting.
Though Singh will receive the first of the 36 Rafale jets on Tuesday, the first batch of four aircraft will come to India only by May next year.
Singh received the aircraft at the Rafale fighter jet handing-over ceremony at Merignac in the presence of French Minister of Armed Forces Florence Parly. Members of the top military brass of France as well as senior officials of Dassault Aviation, the makers of Rafale, were also present at the ceremony.
Addressing a joint media event with Macron, Modi said the two countries have robust cooperation in the fields of defence and security.
Five Rafale fighter aircraft arrived in India from France on July 29 and have started extensive training within 24 hours of touching down in the country. The French-origin fighter aircraft are part of the 17 Golden Arrows squadron of the Indian Air Force.
RM took stock of progress in production of the fighter jets whose delivery to India will begin in September next year.