Française des Jeux is two days away from securing France's first top ten finish since Cyril Dessel's seventh place in 2006.
Christophe Le Mével, who sits ninth overall, just one second ahead of Mikel Astarloza (Euskaltel-Euskadi) and 59 seconds ahead of Vladimir Karpets (Katusha), gained time on the peloton during stage 14 to Besançon and moved up to fifth overall.
Impressive displays in the Alps and a solid ride in yesterday's time trial, where he finished 55th, means he is within touching distance of his aim.
"I feel good and I would like to finish in the top ten when we arrive in Paris," Le Mével told Cyclingnews after today's stage finish.
The 28-year-old, who won a stage of the Giro d'Italia in 2005 and finished tenth overall at Paris-Nice and Dauphiné Libéré this year, has been one of the quieter revelations of this year's Tour de France, with riders Bradley Wiggins and Vincenzo Nibali hogging the limelight.
However, Le Mével has managed to surprise even himself with his strong form in what has widely been agreed as the Tour's toughest week.
"Yes, I've been a little surprised with how I'm feeling in the third week but I've worked very hard to get to this level of strength and fitness."
Le Mével will have to face a brutal stage tomorrow as the race heads towards Mont Ventoux for the Tour's penultimate stage.