Benzema's stunning strike put World Cup holders France in front six minutes after half-time, only for Trabzonspor striker Cornelius to turn in Denmark's equaliser midway through the second half and then smash in an 88th-minute winner.
That meant it was a disappointing night for France who also saw both Kylian Mbappe and Raphael Varane come off with knocks.
There was a near-full house of 75,833 inside the Stade de France, including 1,400 Danish supporters, but the atmosphere outside the ground ahead of kick-off was calm.
That was in stark contrast to the scenes six days earlier, when serious organisational problems led to fans being unable to get into the stadium while many peaceful supporters were tear-gassed ahead of Real Madrid's 1-0 win over Liverpool in the Champions League final.