The unseeded Indians lost 4-6 6-7 (2), squandering as many as eight break chances in the second set and 11 overall.
Indian challenge has now ended in both singles and doubles event.
Simon, who earlier shocked top seed Marin Cilic in singles semi-final and Herbert will now take on second seeded Dutch pair of Matwe Middelkoop and Robin Haase, who defeated Czech team of Jiri Vesley and Roma Jebavy 6-2 6-4 in the other last four clash.
It was far from an ideal start for the Indians with Sharan dropping serve in the second game. It was Simon's lob from back of the baseline that put the Indians down 15-40 and Sharan double faulted on second break chance.
The French remained solid with their service games and In no time the home team was trailing 0-3.
Bhambri's serve was also put under pressure by the French duo but they finally got on board.
Bhambri served the eighth game without fuss to make it 4-4.
Sharan though struggled to hold serve again and was broken in the 10th the Indians lost the set.
Indians had a great chance to get early break when Sharan found service return winner off Simon at 30-30 in the third game but they could not convert with Simon finding a forehand winner after a superb rally with Bhambri.
On the deuce point, Bhambri hit a backhand long.
Under pressure, Sharan and Bhambri saved a match point on former's serve in the next. However, they were outplayed in the tie-breaker.
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