The reform-minded new Indian Prime Minister Modi has been courted by Western governments since his election in May, after being boycotted for a decade over religious riots in his home state of Gujarat.
"It's an honour", said Fabius who stressed the importance of arriving first in New Delhi, "it shows the depth of the ties between India and France."
Fabius is expected to push defence and trade deals including a complicated contract, worth 12 billion dollars, to supply Rafale fighter jets to India.
Other commercial agreements are expected, such as deals to supply new nuclear reactors to India and efforts to boost tourism and space cooperation.
After meeting his counterpart Sushma Swaraj and Defence and Finance minister Arun Jaitley on Monday, Fabius said in a press conference that "talks are going in a positive direction (...) and we are very confident about the final result."
On Tuesday, Fabius is to meet Modi, to conclude his two-day trip to India.