The Danes led by a single goal at the break before pulling away in the second half, with Rasmus Lauge netting 10 goals from 11 shots for the Danes against a French side that battled bravely but came up short.
Denmark's historic third victory prompted the operators of the Oresund Bridge, which runs between Sweden and Denmark, to light it up in the Danish red and white colours immediately after the game.
There was disappointment for Sweden, who co-hosted the tournament with Poland, as they were beaten 39-36 by Spain in the bronze medal game.