Marion Bartoli gave the French a 1-0 lead in the best-of-three series when she beat Anabel Medina Garrigues 6-2, 6-4. Gasquet's win ensured France would finish at the top of Group B, and the doubles match was scrapped.
France last reached the final of the international mixed-team competition in 1998, when Mary Pierce and Cedric Pioline lost to Slovakia.
Bartoli, a 2007 Wimbledon finalist, has had two straight-set wins in singles against Australia and Spain after losing a tight three-set opener to Li Na.
"I'm hoping this kind of level will take me far this year," Bartoli said. "I had a good season in 2011 but I want to get even better in 2012."
The Group A finalist will be determined Friday, with top-seeded Czech Republic -- featuring No. 2 Petra Kvitova and No. 7 Tomas Berdych -- facing the Denmark team of No. 1-ranked Caroline Wozniacki and Frederik Nielsen.
Gasquet has won all three of his singles matches and said he's confident ahead of the final on Saturday.
"It's very good for me to play these kind of guys. They are the best of the world, so I am really happy to win," Gasquet said. "I am playing good, my serve is good. I'm in no pain, so I hope to win the final."