European governments and the United States boycotted him for a decade over religious riots which occurred while he was running his home state of Gujarat. They are now redoubling efforts to make up for lost time.
Japan, which has longstanding ties with Modi, is widely seen as the best poised among Western powers, but Fabius stressed the importance of arriving first in New Delhi.
"It's an honour," he told AFP at the French embassy where he held talks with India-based business leaders. "It shows the depth of the ties between India and France."
He is expected to push a giant but stalled deal to supply 126 French-made Rafale fighter jets to India, which has been under final negotiation since January 2012 and is worth at least 12 billion dollars.
The complicated contract, which involves technology-sharing and the production of most of the planes in India, has been making slow progress through numerous stages of vetting and evaluation.
Other issues include deals to supply new nuclear reactors to India, efforts to boost tourism -- only 300,000 Indian holidaymakers travel to France each year compared with 1.5 million Chinese -- and space cooperation.
As Fabius started his meetings, an Indian rocket blasted off from a south Indian spaceport carrying a French-made satellite built by aerospace group Airbus.
Fabius met Foreign Minister Sushma Swaraj on Monday and will later hold talks with Defence and Finance Minister Arun Jaitley during his two-day trip.After meeting the navy chiefs last week, Jaitley criticised the "slow pace of acquisition" for the defence forces and said there was a "good case for these processes to be expedited".
On Tuesday Fabius is scheduled to meet Modi, who has welcomed leaders from South Asia to New Delhi during his month in office but who has a packed foreign agenda ahead.
He made India's smallest neighbour, Bhutan, his first foreign trip and is expected to travel to Japan soon and then the United States in September.