The 99-mile route from Samatan to Pau was mostly flat, but teams with strong sprinters didn't try to chase down Fedrigo and Christian Vande Velde of the U.S. in the final breakaway.
Fedrigo, of the FDJ-BigMat team, captured a Tour stage for the fourth time in his career. He left a group of six riders with about four miles to go. Only Vande Velde, who rides for Garmin-Sharp, was able to stay close.
Vande Velde tried to outsprint Fedrigo in the last 200 yards, but his rival accelerated to the line to become the fourth French rider to win a stage this Tour.
"It's incredible ... the stars need to be aligned," said Fedrigo, whose last Tour stage win was also in Pau two years ago. "There are days when things go like that."
Fedrigo said the victory was especially satisfying because he was sidelined for six months last year with Lyme disease.
Wiggins finished 11 minutes, 50 seconds behind Fedrigo in the main pack. The 32-year-old Team Sky leader is looking to become Britain's first winner of cycling's showcase race
Overall, Wiggins leads second-place teammate Christopher Froome by 2:05. Vincenzo Nibali of Italy is third, 2:23 behind. Defending champion Cadel Evans remains fourth, 3:19 back.
Wiggins said he and other riders were looking forward to Tuesday's rest day.
"A lot of people are tired now -- mentally more than physically," he told French TV. "It was hard today nonetheless, it was quite hot. And the road was hilly."
The rest day comes before two punishing days in the Pyrenees. The rides, along with a final time trial in the next-to-last stage, are likely to determine the winner of the three-week race, which ends July 22 in Paris.
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