He also met Minister for the Armed Forces, Ms Florence Parly and the Defence Advisor to the French President, Admiral Bernard Rogel.
After receiving the jet, he will take a sortie in it. He will also perform the traditional Shastra Puja in Paris as the day is coinciding with the Hindu festival of Dussehra.
After his talks with Macron at the Elysee Palace in the French capital, Singh will be flown to Merignac, a suburb of the south-western French town of Bordeaux, where he will participate in the official handover ceremony for the first Rafale combat jet acquired by the Indian Air Force (IAF).
The ceremony coincides with the foundation day of the Indian Air Force as well as the day when Dussehra will be celebrated.
Arrangements have been made at the air base for a traditional 'Shastra Puja', or weapons' worship which forms part of Dussehra celebrations. After performing puja, Singh will take a sortie in a two-seater trainer version of the aircraft.
"Raksha Mantri will participate in the Rafale fighter aircraft handing over ceremony at Merignac along with French minister of Armed Forces Florence Parly," a ministry of defence spokesperson said.
"He will also perform the Shastra Puja on the auspicious occasion of Vijayadashami and fly a sortie in the Rafale fighter aircraft, the spokesperson said.
Members of the top military brass of France as well as senior officials of Dassault Aviation, the makers of Rafale, will also be present at the ceremony.
India had ordered 36 Rafale fighter jets from France in a deal worth Rs 59,000 crore in September 2016. While the formal handover ceremony takes place this week, the first batch of four Rafale jets will fly to their home base in India by May 2020.
All 36 jets are expected to arrive in India by September 2022, for which the IAF has been reportedly undertaking preparations, including readying required infrastructure and training of pilots.
The handover ceremony will be followed by the annual Indo-French Defence Dialogue between Singh and French Armed Forces Minister Florence Parly back in Paris on Tuesday evening.
On Wednesday, the minister is scheduled to address CEOs representing leading French defence industry enterprises. As part of a wider 'Make in India' message, Singh will invite them to participate in the DefExpo to be held in Lucknow from February 5 to 8 next year.
(With inputs from PTI)