Coquard was able to pip Elia Viviani to the finish line in South France.
Froome finished in 70th place, 56 seconds behind the current leader.
The British rider is making a comeback after surgery and rehabilitation following a huge crash in last year's Criterium du Dauphine.
He is attempting to challenge for Team Ineos for the Tour de France but may lose out to Colombian teammate Egan Bernal, and he will join Israel Start-Up Nation next season.
Bryan Coquard of France and Team B&B Hotels - Vital Concept / Celebration / during the 44th La Route d'Occitanie - La Depeche du Midi 2020, Stage 1 a 187km stage from Saint Affrique to Cazouls lès Béziers
Image credit: Getty Images
During the race, temperatures reached 39 degrees celsius as the riders had to endure gruelling circcumstances.
It was down to Andreas Lorentz Kron of Riwal Readynez and Marti Marquez of Kern Pharma to battle it out of the best climber jersey, with Lorentz Kron in second in the breakaway after the Tres Vents pass, with Marquez ahead of him.
25 kilometres from the finish, Lorentz Kron was joined by Lilian Calmejane (Total Direct Energie) as the broke ahead of the peloton with a 40 second lead, though that lead was quickly whittled away by the pack who pulled them back in.
With a concentrated bunch racing to the finish, a late charge saw Viviani (Cofidis) push Coquard (B&B Hotels - Vital Concept P/B KTM) to the line but the Italian could not claim the win.
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