Home hope Bardet out as crashes cause Tour de France chaos
Bardet and English rider James Shaw fell at sped downhill after the day's first climb.
A runner-up at the Tour de France and world championships, Bardet had been in 12th overnight and was targeting an overall finish in the top five and a stage win.
Ahead of the stage, the series of Alpine descents had put Gino Maeder's recent fatal crash in the Tour of Switzerland firmly in the minds of many in the peloton.
Earlier, after a sudden shower, there was a mass fall on a corner just 5km into stage 14 that forced organisers to halt the race for 25 minutes.
Up to 25 riders fell and 50 were blocked with about a third of those who hit the tarmac at 50kph struggling to get back in the saddle.
The race restarted 24 minutes after the fall.
South African rider Louis Meintjes, 13th overall, suffered a broken collarbone and did not rejoin the race. Spaniard Antonio Pedrero was evacuated on a stretcher and Colombian Esteban Chaves restarted but pulled out ten minutes later.
Neither of the race favourites, Jonas Vingegaard and Tadej Pogacar, were involved. During the wait, Pogacar dismounted and sat chatting on a kerbside.