The score was tight throughout the game at Rio's Future Arena, where a mostly France-leaning crowd chanted for their "Bleus", but the Danes managed to pull ahead, in part thanks to brilliant saves by 2.01 metre-tall keeper Niklas Landin.
When the breakneck game was finally over, the Danish team poured onto the court hugging, high-fiving, and clasping their hands on their heads in disbelief.
"It was just perfect to finish it off like this,” said Denmark's Mads Christiansen, gold medal hanging around his neck after the game, adding it was especially sweet to beat the defending champions.
For the French, who won gold in London 2012 and Beijing 2008, defeat to the Danish underdogs was bitter. It came a day after the French women also lost the final, settling for silver against Russia.
Earlier on Sunday, Germany's men's team overcame Poland 31-25 to win bronze.
(Reporting by Alexandra Ulmer; Editing by Alison Williams)
