Musetti, who qualified for his third semifinal appearance of the season, outsmarted his French opponent with 32 winners in the quarterfinal match.
"Yesterday's match [against Philip Sekulic] gave me a lot of confidence, and today I started very well," Musetti said. "A really solid performance from the baseline and I am really happy to be in the semifinals."
At the Zhuhai Championships, Aslan Karatsev secured a place in the semifinals, beating Cameron Norrie 7-6 (5), 7-6 (5). Karatsev beat former top-ranked Andy Murray in the second round and followed it with another aggressive brand of tennis to beat Norrie in 2 hours, 23 minutes.
"It was very tough," Khachanov said. "A mental and physical match. ... I had to try to push and bring all the energy to change the momentum."
Khachanov plays Sebastian Korda in the semifinals. The American beat fifth-seeded Tomas Martin Etcheverry 6-1, 6-2 in a one-sided quarterfinal match. Japan's Yoshihito Nishioka beat Germany's Jan-Lennard Struff 6-4, 7-5.