Lucas Pouille throttled Belgium's Steve Darcis 6-3, 6-1, 6-0 in Sunday's decisive fifth rubber to clinch a 10th Davis Cup title for France in front of a passionate Lille crowd.
Belgian ace David Goffin levelled the final at two points apiece after beating Jo-Wilfried Tsonga in straight sets in Sunday's opening reverse singles, but a revitalised Pouille propelled France to a first victory since 2001.
Pouille was beaten convincingly by Goffin in Friday's first singles tie, but the world number 18 shook off that defeat to swat Darcis aside in one hour and 34 minutes.
"There's nothing better than winning as a team, with my mates, in front of the fans, my family and my friends," Pouille told French television.
"We're going to celebrate and make the most of it. I'm proud of my team."
France's triumph received a presidential seal of approval, with French head of state Emmanuel Macron posting on Twitter: "Bravo to all the winning team which has made all of France proud."
It was a third victory as captain for Yannick Noah, who returned for a third stint in charge in 2015 after two spells as skipper in the 1990s.
Noah, the last Frenchman to win a Grand Slam tournament at the 1983 French Open, was vindicated in his selection after surprisingly picking Richard Gasquet to partner Pierre-Hugues Herbert for Saturday's crucial doubles victory.
"To have four different players win the three points is great," an emotional Noah told BeIN Sports.
"Everyone wanted this, we favoured the spirit of the group above individuals... I'm so happy."
Pouille broke Darcis, who had sent Belgium through to the final by winning the deciding rubber against Australia in September's semi-final, at the first attempt to lay the foundation for a memorable triumph.
That proved enough to wrap up the first set, with three further breaks in the second firing Pouille and France to the brink of the title.
Darcis, the world number 76, was powerless to stop a rampant Pouille as the 23-year-old dismantled the Belgian in the third set -- winning 25 of 34 points -- to end France's run of three straight finals defeats.
Belgium's hopes of claiming a first title in the venerable competition rested with their in-form number one Goffin, who downed Tsonga 7-6 (7/5), 6-3, 6-2 after withstanding sustained early pressure.
Goffin saved a set point while serving at 5-6, as Tsonga was left to rue his inability to capitalise on any of six break points in a marathon first set.
World number seven Goffin, the runner-up to Grigor Dimitrov at the season-ending ATP Finals in London last weekend, snatched a 75-minute opening set with a blistering backhand return in the tie-break.
Tsonga, who brought France level in Friday's second singles with a crushing win over Darcis, then surrendered his serve in the second set with a costly double fault as Goffin surged 4-2 ahead before seizing a two-set lead.
Goffin stormed to a double-break lead in the third set as Tsonga's resistance crumbled, and closed out the match with minimal fuss, but Darcis was unable to reproduce previous heroics against an inspired Pouille.
France drew level with Britain after securing a 10th title -- a tally only surpassed by the US, the record 32-time champions, and Australia, on 28 titles.
France had appeared in three finals since last lifting the trophy -- in 2002, 2010 and 2014 -- with both Tsonga and Gasquet part of the team beaten three years ago by a Switzerland featuring Roger Federer and Stan Wawrinka.
"It's great for me to be finally able to win it, I've been chasing after it for 10 years," Tsonga added. "I put other things to one sides to be able to play and win this competition. I'm really so happy."
Belgium were appearing in just a third Davis Cup final -- after 1904, and 2015 when they lost to Andy Murray's Britain in Ghent.
Losing captain Johan Van Herck said: "We did everything to win and ultimately it didn't come off.
"We knew it was going to be very tough."