Fritz is set to face either Jannik Sinner or Casper Ruud in the final on Sunday.
World No. 3 Alcaraz beat Rublev 6-3, 7-6 (10/8) to lift himself off the bottom of the John Newcombe Group.
Alexander Zverev opened his campaign at the ATP Finals in Turin on Monday evening by dispatching Andrey Rublev 6-4, 6-4 in their round-robin opener.
Alcaraz could be eliminated if he loses to second-ranked Alexander Zverev, who faces Andrey Rublev in his opener later on Monday.
Rafael Nadal and Casper Ruud saved a match point in the deciding set tie-break to reach the semi-finals of the doubles in Bastad on Wednesday, hours after the Norwegian was knocked out of the singles.
It was Nadal's first match since the 38-year-old fell to Alexander Zverev in the opening round at Roland Garros on May 27.
Carlos Alcaraz defeated Australia's world number 69 Aleksandar Vukic 7-6 (7/5), 6-2, 6-2 on the back of 42 winners.
Alexander Zverev holds a career 5-4 winning record against Carlos Alcaraz, including a victory in their only previous Roland Garros meeting in the 2022 quarter-finals.
Alexander Zverev advanced to his fourth successive French Open semi-final with a 6-4, 7-6 (7/5), 6-4 win over Australian 11th seed Alex de Minaur on Wednesday.
Casper Ruud continued his bid to reach a third straight French Open final with a four-set victory over American Taylor Fritz in the last 16 on Monday, setting up a meeting with Novak Djokovic.