Veteran duo Julien Benneteau and Nicolas Mahut secured France's decisive win, beating Feliciano Lopez and Marcel Granollers 6-0, 6-4, 7-6 (9/7).
It was the second Grand Slam title for the top-ranked pair of Pierre-Hugues Herbert and Nicholas Mahut after their triumph in the 2015 US Open
Jo-Wilfried Tsonga, Gael Monfils, Richard Gasquet, Julien Benneteau and Gilles Simon had been recalled after helping France beat the Czech Republic 4-1 in the semi-finals in September.
David Ferrer needed just 71 minutes to seal the victory and give himself a shot at adding a second title of 2014 to the trophy he lifted in Buenos Aires.
Swiss Stanislas Wawrinka goes on to tackle France's Julien Benneteau, who put out Poland's Jerzy Janowicz 7-5, 6-1, for a place in the semifinals.
Julien Benneteau, 32, advanced with a 6-1, 6-2 victory over the former top-ranked Lleyton Hewitt. He had to adjust on the fly after the second rain delay, which lasted two hours.
Haase, 26, explained in the daily Volkskrant that, after undergoing the test, he received a letter from the ATP advising him "to get a lawyer" and indicating that he would have to undergo three more tests in the following two weeks.
The second-seeded German, won also won the event 12 years ago, maintained his slim chance of qualifying for next month's ATP finals in London.
The unseeded Sousa defeated fifth seed Julien Benneteau of France 2-6, 7-5, 6-4 in the final.
Tipsarevic has had a dreadful run this season as he has slipped out of the top 10 in a downward trend which has accelerated over the last four months.