The 136-mile Stage 12 produced no change at the top of the overall standings. Froome still has his big lead of more than three minutes over his main rivals, who are hoping to claw back time on climbs up Mont Ventoux on Sunday and in the Alps next week.
Froome narrowly avoided a pileup that floored about 20 riders just behind him on the road into Tours. The escape demonstrated that to win the Tour, a rider must be lucky as well as strong.
Teammate Edvald Boasson Hagen was among those brought down. Sky later announced his withdrawal from the race with a broken right shoulder. That leaves Froome with six teammates — from the eight he started with on June 29 — to shepherd him through the last 10 days. Sky's Vasil Kiryienka missed the time cut on Stage 9.
"It's never nice to lose a rider of Edvald's ability," Brailsford said. "But ultimately we're still confident that with the riders we've got left we can pull together and see the race through."