India chose Dassault Aviation's Rafale for exclusive negotiations over a year ago to supply 126 aircraft in a deal potentially worth $10 billion.
However, both sides have played down prospects that the deal would be finalised when President Francois Hollande visits India on February 14-15.
"Things seem - I'm very cautious - to be looking very positive. That's at least what the Indians say," Fabius said in an interview on BFMTV.
He added that recent talks with his Indian counterpart and subsequent contacts had gone in the right direction.
Indian Defence Minister A.K. Antony pledged on Wednesday not to let defence cuts disrupt efforts to finalise the deal.