Le Drian's comments came after the Indian Defence Ministry said this week it had agreed with the French Defence Ministry to fast-track negotiations and seek to overcome differences in talks that have been ongoing since January 2012.
"We are in a positive process, I hope it will come to a successful conclusion. It has progressed well," Le Drian told BFM-TV.
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Le Drian said it would not happen before the end of the year, however.
"It's not three weeks ... it's several months, we'll see. But I'm optimistic."
Last month, the CEO of Dassault Aviation told Reuters a contract by the end of March was a "reasonable goal." France's Dassault has been trying to clinch a deal to sell India its Rafale jets since New Delhi chose the company over other foreign plane manufacturers in 2012.
Disagreements over cost and work-sharing slowed talks, as well as elections in India.
Under the deal, which would provide a major boost to French domestic defence manufacturing, the first 18 planes will be made in France and shipped to India, while the remaining 108 will be produced by state-run Hindustan Aeronautics Ltd.