Pouille was never threatened in the decisive rubber after David Goffin had given Belgium both their points with impressive displays in the singles.
Les Bleus, however, had more strength in depth, winning a singles match through Jo-Wilfried Tsonga on Friday and Saturday's doubles with Richard Gasquet and Pierre-Hugues Herbert.
It was their first title since they beat Australia away in 2001 before three defeats in the final - in 2002, 2010 and 2014 - while Belgium have yet to win the title, having now lost three finals after defeats in 1904 and 2015.
Yannick Noah, the last Frenchman to win a grand slam title, celebrated his third Davis Cup success as captain after leading France to victory in 1991 and 1996.
"It was a victory we had been dreaming off," said Noah. "It's a united group. It was a tough weekend against a good Belgian team. Lucas played a fantastic final match."
Belgium captain Johan Van Herck added: "I would not change anything. We have regrets about losing, it's normal that we are disappointed after a tough weekend. In sports it's never nice to be second".
STRAIGHT SETS
Goffin gave the visitors a 1-0 lead by beating Pouille in the opening singles before Tsonga levelled by defeating Darcis on Friday, the number ones both prevailing in straight sets.
France took the lead thanks to the pairing of Gasquet and Herbert, who had never played a competitive match together but beat Ruben Bemelmans and Joris De Loore in four sets.
Goffin was again a notch above the rest on Sunday, levelling the tie at 2-2 against Tsonga with a 7-6(5) 6-3 6-2 win as the world number seven sent the tie into a decider.
The final match was anti-climactic as Pouille went for the throat, racing to a 3-0 lead against Darcis, who never seemed to stand a chance on the indoor hardcourt even if he had won all of his five matches in the competition before.
World number 18 Pouille, who was born 75 km from Lille, held serve to take the first set and never looked back, claiming 12 games in a row and closing it out on the first match point when a sorry Darcis sent a shot long.
"There's nothing more beautiful than winning as a team in front of my friends and family. Now we're going to celebrate and enjoy it," said Pouille.
(Reporting by Julien Pretot; Editing by Clare Fallon and Ken Ferris)
