The Indo-Swiss pair went down in one hour and 21 minutes on Sunday night.
Sania-Martina were eyeing their 14th title together. They were aiming for their first title since February but were undone by a stunning turnaround by the French pair.
Sania-Martina began the match brightly, winning the first set comfortably 6-2.
But the French duo recovered from a set down to clinch the match in the tie-breaker. They were the more aggressive team, hitting 25 winners to 16 by Sania-Martina.
It was the second title of the season for the French pair.
Sania and Martina have stumbled in their recent tournaments, exiting in the second-round at the Miami Masters and the first at the Indian Wells.