Froome was knocked off his bike after stage 17 of the Tour de France on Wednesday.
He struggled after the stage to get his words out.
Thomas went straight over to his wife Sarah Elen after finishing another day of cycling knowing Sunday should be a glorious day.
Demare said he was motivated by an accusation on social media from Andre Greipel, a top German sprinter, who alleged that Demare held on to his team auto on the way up the grueling Col de Portet in Stage 17.
"I'm really trying not to cry, it's unbelievable".
A former ski jumper who rides for Team Lotto NL-Jumbo, Roglic finished 19 seconds ahead of Thomas, while Romain Bardet of France crossed third with the same time.
Froome had been the favorite to retain his title but he paid the price for the efforts he made to win the Giro d'Italia in May as he just failed to become the first man in 20 years to achieve the Giro-Tour double. "It's not going to be easy, but I do get to wear my French time trial champion's jersey".
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Demare, who failed to make the cut on a climb in the Alps a year ago, had time to celebrate as he crossed the line with his arms wide open ahead of fellow Frenchman Christophe Laporte.
Thomas had survived Friday's big test, a 200.5-kilometre stage from Lourdes to Laruns which took the peloton over three of the toughest Pyrenean climbs - the Aspin, Tourmalet and Aubisque.
Stage 18 saw local hope Demare, who had been accused by fellow sprint specialist Andre Greipel of holding on to his team auto in Wednesday's mountain stage to avoid missing the time cut, perfectly set up by Italian team mate Jacopo Guarnieri.
Intermittent rain, the first significant downfall of the entire Tour, created unpredictable conditions on Saturday's 31km course.
Thomas may have known he had a buffer to play with but he was not taking it easy as he was fastest through the first and second splits before grinding up the Col de Pinodieta and dropping back.
Vincenzo Nibali will undergo surgery next week on the back injury he suffered during a crash in the Tour de France as Arnaud Demare silenced his critics by claiming a comfortable win in the bunch sprint of the 18th stage.
Geraint Thomas takes a two-minute lead into the time trial. It was stressful, though, because this morning I could not find my (world champion) rainbow jersey suit and I had to ask my sponsor to give me a new one at the last minute.