Gasquet, seeded third, will next play Jarkko Nieminen of Finland, who advanced to the last four with a 4-6, 6-3, 7-6 (2) victory over Sergiy Stakhovsky of Ukraine.
Benneteau, seeded sixth, needed treatment on his back early in the third set and was clearly impeded afterward. He barely moved in trying to reach Gasquet's passing shot down the line on match point.
Michael Llodra and eighth-seeded Benoit Paire also won quarterfinals and will meet in Saturday's other semifinal to guarantee a French finalist.
Llodra hit 11 aces in a 7-6 (3), 6-1 win against Jan Hajek of the Czech Republic, sealing the victory with a volley at the net. Paire beat fourth-seeded Gilles Simon 7-5, 7-6 (4) in another all-French match.
"It's not easy to play a friend, we were both very tense on the court," said Paire, who also made his second semifinal this year after reaching the last four in Chennai, India. "I'm happy that I managed to stay focused on my match."
Simon broke in the seventh game for a 4-3 lead but Paire broke straight back and saved a break point in the next game before taking control. He opened a 5-2 lead in the second set.
Serving for match, Paire double-faulted and Simon forced a tiebreaker.
"Benoit's aggressive on second serve," Simon said. "He had a lot of opportunities on my second serve and hurt me with that."