Bardley Wiggins claimed the first Tour title for Britain a year ago but a series of physical problems, including a knee injury, forced him out several weeks before the 2013 Tour de France -- the 100th in the series.
Froome finished second to his teammate Wiggins last year in the general classification. With Wiggins sidelined, Froome became the lead rider for UCI ProTeam Team Sky.
Saturday, Froome took control of the race's eighth stage, winning by 51 seconds after a strong showing on a late climb. He also took over the overall lead -- leading teammate Richie Porte by 51 seconds.
After Sunday's Stage 9, Froome's overall lead grew to 1 minute, 25 seconds, even as he was 14th in the stage, 20 seconds off the winning time of Daniel Martin.
In the general classification in which the first week's overall lead was never more than 3 seconds, an 85-second advantage makes Froome, 28, the strong favorite to win his first Tour de France and give Britain its second Tour champion.
The riders had a rest day -- the first of two this year -- Monday before heading to Saint-Gildas-des Bois in northwestern France to begin a 122.4-mile ride Tuesday to Saint-Malo over a relatively flat route.
The rest of the week's schedule includes an individual time trial Wednesday, with flat stages Thursday and Friday before mountain routes near the Alps over the weekend.