Belgium recovered from a 2-1 deficit to triumph on the indoor clay of the Palais 12 in Brussels.
Jo-Wilfried Tsonga had earlier sent the French team to their 18th final by defeating Serbia’s Dusan Lajovic 2-6, 6-2, 7-6 (5), 6-2 in Lille. France will host the final from 24-26 November.
With Tsonga’s win, the French established an unassailable 3-1 lead and the teams decided against playing the final rubber.
Belgium had trailed after Saturday’s doubles but they turned things around in front of a buoyant crowd. Goffin first rallied past Nick Kyrgios 6-7 (4), 6-4, 6-4, 6-4 before Darcis defeated Jordan Thompson 6-4, 7-5, 6-2.
Goffin, who had not beaten Kyrgios in three previous matches, returned well and played astute tennis to counter his opponent’s big shots, extending his excellent Davis Cup record to 15 wins from 16 singles matches.
Goffin dropped his serve only once and hit two aces in succession to serve out the match after a three-hour battle.
“Everything is in the timing, I think,” Goffin said about his returns, adding: “I see the ball earlier than the others so maybe that’s why I have a good return.”
Darcis was set to take on John Millman in the decisive rubber but Australia captain Lleyton Hewitt changed his line-up and sent out Thompson instead. The move failed to pay off as Darcis deliverd a dominant display, converting five of seven break points. He hit 34 winners and sealed the match on his first chance with a backhand volley that hit the net cord.
France avenged their loss to Serbia in the 2010 final and qualified for their first final since losing to Switzerland in the title match three years ago.
The French won the last of their nine titles in 2001 against Australia, while Belgium, who were beaten by Great Britain in the 2015 final, have never lifted the trophy
“I’m relieved and happy,” said France captain Yannick Noah. “To win the Davis Cup is something extraordinary. Hopefully I will be able to win it with theses lads.”
Noah previously captained France to the 1991 and 1996 Davis Cup titles. As a player, he also won the French Open in 1983.
The French did a lap of honour after Tsonga won the decisive point against a depleted Serbian team that gave the hosts a tough challenge. Tsonga won his second point for France after defeating 22-year-old debutant Laslo Djere in straight sets on Friday to level the tie at 1-1.
Two-time Grand Slam champions Nicolas Mahut and Pierre-Hugues Herbert then gave the hosts a 2-1 lead when they beat Filip Krajinovic and Nenad Zimonjic in the doubles match.
Tsonga, who had decided to skip the Davis Cup this year, changed his mind and made a successful return to the French team.
He was overpowered by his rival in the first set but improved and recovered in the second by upping his game when it mattered, after a double fault by Lajovic gave him an early break.
The third set was close with neither player giving in on the red clay of the Pierre Mauroy stadium. Lajovic was the first to crack despite saving two set points in the tie-breaker when he dumped a backhand return into the net.
Tsonga missed three break chances in the opening game of the fourth set but converted the fourth after Lajovic made two consecutive unforced errors – a double fault and a forehand in the net. The Frenchman then held to love and broke again as Lajovic showed signs of fatigue following his five-set win over Lucas Pouille on Friday. Tsonga then served out the match.