France took the lead through Karim Benzema at the Stade de France, the venue where he lifted the Champions League with Real Madrid six days earlier, but they were unable to see out the win.
Trabzonspor striker Cornelius volleyed in a delightful equaliser and then fired in a winner two minutes from time to stun France, who lost Kylian Mbappe to a first-half injury.
Denmark join Austria, who beat Croatia 3-0 elsewhere on Friday, at the top of Group A1.
The visitors enjoyed a near-perfect campaign in qualifying for Qatar 2022, where they will meet France in the group stage, and started the brighter in this contest.
Kasper Dolberg got in behind the home defence inside the first three minutes and picked out Joakim Maehle, who hit the outside of the post with the angle against him.
France soon grew into the game, with Benzema having a goal-bound shot blocked by Jannik Vestergaard and a low strike past Kasper Schmeichel ruled out for offside.
Mbappe sustained an injury shortly before half-time and played no part after the break, but Didier Deschamps’ men did not require long to open the scoring in the second half.
Benzema played a one-two with Mbappe’s replacement Christopher Nkunku, took the ball past three opposition players and slid the ball away from Schmeichel for the 51st-minute opener.
Les Blues did not build on that lead, however, as Cornelius flashed a first-time finish past Hugo Lloris in the 68th minute with the side of his boot after being spotted by Pierre-Emile Hojbjerg.
N’Golo Kante hit the post with a curled effort, but it was Cornelius who had the final say in Paris with a thumping finish into the roof of the net at Lloris’ near post.
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