Tsonga, 12th in the ATP Race to the World Tour finals and with an outside chance of qualifying for the season-ending event, needed to reach the last four to add to his points tally.
The Open de Moselle is a third-tier event that would have given Tsonga 250 points had he won the title, helping him boost his chances of taking part in the Nov. 9-16 London tournament.
The top eight players in the Race qualify and Tsonga trails eighth-placed Tomas Berdych of the Czech Republic by 885 points.
The world number 11 had reached the Metz final in his three previous participations in the event, winning the title in 2011 and 2012, and losing in the final last year.
Tsonga helped France qualify for the Davis Cup final last weekend, winning his singles and doubles matches as Les Bleus defeated holders Czech Republic.
Eighth seed Goffin will next face German Jan Lennard Struff who went through after compatriot Philipp Kohlschreiber abandoned with a possible shoulder injury.
(Reporting by Julien Pretot; Editing by Justin Palmer)
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