The 24-year-old Calmejane, in only his second year as a professional, dropped his breakaway companions in the last climb of the day and despite cramping up in the closing stages, held off Dutchman Robert Gesink for a second grand tour stage win.
Another Frenchman, Guillaume Martin (Wanty-Groupe Gobert), took third place.
Britain's Chris Froome had a minor scare when he went off the road in a descent, but the Team Sky rider kept his cool in sweltering heat to retain the overall leader's yellow jersey.
"Me and (team mate) Geraint (Thomas) took the wrong trajectory in a corner and we went off the road, it happens sometimes," said Froome.
Thomas crashed but he was quickly back on his bike.
Calmejane of Direct Energie kept his strategy close to his chest in the day's breakaway, but barely looked back after pulling away in the 11.7-km climb to La Combe de Laisia.
Gesink (LottoNL-Jumbo) chased hard but the Frenchman had too much power in the finale.
Calmejane, almost came to a halt five kilometres from the line, however, due to cramp in his right thigh.
"It's huge. It was everything I was dreaming of," said Calmejane, who won a stage in last year's Vuelta.
"When I had cramp in the finale, I decided to drop a gear so I could pedal softer," he said.
"I suffered like never before," added Calmejane, who snatched the polka-dot jersey as mountains leader.
Team Sky were in control all day despite a hectic start to the stage, with almost 50 riders managing to break away from the main pack.
Ireland's Dan Martin attacked from the pack in the finale but the Quick-Step Floors rider, fourth overall, was quickly reined in.
They will be further tested on Sunday, when the ninth stage takes the peloton through the Jura mountains with three lung-busting climbs in prospect before a dangerous descent to Chambery.
"Tomorrow will be a very very hard day, it will be very selective," said Froome ahead of a stage that features 4,700m of climbing.
Froome holds a 12-second lead over Thomas with in-form Fabio Aru of Italy in third place, 14 seconds off the pace.
(Reporting by Julien Pretot; Editing by Jon Boyle and Clare Lovell)
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