Herbert has a career Grand Slam in doubles but in singles is ranked 93rd, compared to fifth for the Australian Open semifinalist Tsitsipas.
But the clean-serving Frenchman turned the tables on the big-serving Greek by effectively using serve and volley on the indoor hard-court. He hit eight aces to two, won 79% of his first serves compared to 64% for second-seeded Tsitsipas, and clinched victory with a smart backhand volley at the net.
A French finalist is guaranteed, too, since Herbert plays the winner of the late match between fourth-seeded Ugo Humbert and Arthur Rinderknech, a qualifier ranked 138th.
The imposing Russian saved the only break point he faced and broke the Italian player’s serve three times at the indoor tournament.
The Australian Open runner-up has won 21 of his last 23 matches and will climb to second in the ATP rankings next week.
“It is my first time here in the semifinals in Marseille… I was on top of the match the whole time,” Medvedev said. “Jannik always tries to hit the ball as hard as he can. You cannot give him easy balls, otherwise you are going to run all over the place and he is probably going to hit a winner.”
When the two-time Grand Slam runner-up climbs to No. 2 on Monday, he will be the first outside the Big Four of Roger Federer, Rafael Nadal, Novak Djokovic and Andy Murray to do so since Nadal in July 2005.
Medvedev is chasing a 10th career title and next faces qualifier Matthew Ebden, who at No. 287 became the lowest-ranked semifinalist in the tournament’s 28-year history.
Setting the tone for upsets, the Australian downed third-seeded Karen Khachanov 4-6, 6-4, 6-2, breaking the Russian four times.