After two second-place finishes, Edvald Boasson Hagen finally got a stage victory at the Tour de France.
Bardet had a mediocre time trial and the AG2R-La Mondiale rider, runner-up a year ago, salvaged a podium finish by one second to finish third, 2:20 off the pace, with Froome's Spanish team mate Mikel Landa taking fourth place.
Stage 19, which is also the longest of the Tour de France presents itself as the flawless opportunity for the breakaway, with a mainly flat 222.5-kilometre journey ahead of the peloton.
It's been an interesting Tour de France for cycling fans - Mark Cavendish was forced to pull out after breaking his shoulder, a controversial crash saw Slovak Peter Sagan kicked out of the competition, and Chris Froome looks to be heading for yet another victory.
Britain's Froome now looks nearly certain to stand on the Paris podium in the yellow jersey for the third year in a row after suffering no mishaps on a hot and sweaty 222km ride out of the Alps into Provence.
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"It was a really fantastic day for me today", Bodnar said.:I've waited a long time for this moment, for my first stage victory at the Tour de France.
Barring a disaster on the ceremonial final stage of the Tour de France, Chris Froome will become a four-time victor of the race on Sunday, clinching his third successive victory on the Champs-Elysees.
Bodnar, taken in the straight line final of Pau (stage 11) after a long break, won for the first time in the Tour.
World time trial champion Tony Martin was the first to go close, but the German rider was 14 seconds adrift.
Only three riders held the yellow jersey during this year's iteration of the Tour.
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Neither Froome nor Uran will likely win Stage 20, but their battle is the one to watch regardless. It's been a hard tour for the team.
The versatile Norwegian, riding for the African-based Dimension Data team, was part of a nine-man lead group speeding towards a roundabout 2.5km from the finish line of the 222km trek from Embrun on stage 19.
Team Sky boss Dave Brailsford heaped praise on the 32-year-old.
Last year, Froome won by four minutes and five seconds ahead of Frenchman Romain Bardet. "I'll do my maximum for sure", he said.
"I'm in Paris waiting for the finish now, but I've watched every stage microscopically and it has been an awesome Tour for us", Drapac told The Australian Financial Review.
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