The 158.5-kilometre (99-mile) route from Samatan to Pau had a mostly flat layout, but teams with strong sprinters didn't try to chase down the breakaway riders.
Fedrigo, of the FDJ-BigMat team, collected his third Tour stage win by leaving a group of six riders with about 6.5 kilometres (4 miles) left, with only Garmin-Sharp rider Christian Vande Velde of the United States able to stay close.
Vande Velde made a brief burst to try to outsprint Fedrigo in the last 200 metres, 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."
Wiggins finished in the main pack more than 11 minutes back.
Tuesday is a rest day before two tough days in the Pyrenees. The three-week race ends July 22 in Paris.