Tsonga, who brought France level in Friday's second singles with a crushing win over Steve 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.
Being outplayed by Tsonga was no shame for Darcis, but for a man who had never lost a deciding match in the Davis Cup before, the thrashing he received from Pouille, who had never before played a decisive rubber, was less expected.
It is their first title since they beat Australia away in 2001 before three defeats in the final in 2002, 2010 and 2014.
Pouille kicked off the hosts' quest for the trophy on Friday, while losing to Belgium's top-ranked David Goffin in straight sets. The match, though, was already long lost for the world number 15, who was simply beaten by a much better player on the indoor hardcourt.Tsonga started aggressively, setting up a break point on Goffin's first service game but the Belgian staved it off confidently. France won the tie 3-2 on aggregate.More news: European Union renews licence for controversial herbicide glyphosate for 5 years
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"I'm proud of my whole team and I am sure that we will win the Davis Cup together one day", said team captain Johan Van Herck, after Belgium again failed to break their Davis Cup duck following losses in the 1904 and 2015 finals.
Joalukas Noah was in the depths of the stade Pierre Mauroy to attend the victory of the team of France of tennis coached by his father Yannick Noah.
France tied with Great Britain at the third place for the most number of Davis Cup titles by winning thier tenth crown on Monday.