France took the lead in the mixed team event as Richard Gasquet beat Jack Sock 6-3 5-7 7-6 (8-6) in the men's match.
But the United States levelled thanks to Coco Vandeweghe's 6-4 7-5 win over Kristina Mladenovic in the women's tie.
That set up a deciding doubles match, with Gasquet and Mladenovic triumphing 4-1 4-3 (5-0) to deny the United States what would have been a seventh title.
France's only previous success in the Hopman Cup came in 2014, when Alize Cornet and Jo-Wilfried Tsonga beat the Polish duo of Agnieszka Radwanska and Grzegorz Panfil.
Great Britain had a team in this year's competition but Dan Evans and Heather Watson went out in the group phase after losing against Switzerland, France and Germany.
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France won the Hopman Cup for the second time after beating the United States in the final in Perth.