Porte crashed on the descent from the Mont du Chat, the last of the day's big climbs, as he slid off the inside of corner and was violently flung across the road, with Quick Step Floors rider Dan Martin unable to avoid him.
His team Racing BMC say he has been taken to hospital.
The Col de la Biche was the first of three hors categorie climbs to be tackled on a brutal day of racing through the Jura mountains. He held a 25-second gap as the yellow jersey group rode fast to the site of Porte's race-changing crash.
Bardet, riding on familiar roads - his AG2R-La Mondiale team is based here - attacked on the final descent and got clear.
A storm disturbance in the Atlantic could impact SC
THE ALABAMA WEEKEND: For the weekend, no major change in the pattern and we are going to stick with the standard summer forecast. On the present forecast track, Tropical Depression Four will likely pass a safe distance to the north of the islands on Sunday.
Fuglsang, the recent victor of the Criterium du Dauphine, led out the final sprint before Uran - no longer hampered by that gearing issue - powered past.
Barguil, seemingly back to his best after fracturing his pelvis in the Tour of Romandie back in April, punched the air in celebration believing he had pulled off the impossible; when he was told by his Sunweb team that a maiden Tour win was his, the 26-year-old burst into tears of joy.
Colombian Rigoberto Uran (Cannondale-Drapac) won Sunday's dramatic stage, a 181.5-kilometre route from Nantua to Chambéry. He is now eighth overall, a massive 2:13 off the pace.
However, he suffered his fourth crash of the race on Sunday and was forced to abandon, having suffered a similar fate at the Giro d'Italia earlier this year, when a crash caused by a police bike, also on stage nine, caused injuries which ultimately forced him to withdraw a few days later. Other riders out include LottoNL-Jumbo's Robert Gesink.
Twice former victor Alberto Contador was one of the big losers on the day from the 181.5km stage from Nantua to Chambéry.