He will face Kwon Soon-woo, who upset No.2 seed Alexander Bublik 3-6 7-5 6-3.
Elsewhere, No.1 seed Hurkacz defeated German qualifier Peter Gojowczyk 6-4 7-6 (7-4) to stand on the brink of a third title of the year.
The world No.13 from Poland won 79 per cent of the points on his first serve and sealed victory in an hour and 37 minutes.
Gojowczyk saved five break points but was unable to pull off an upset in Metz.
Hurkacz said: "Peter played a really great match. He was super tough to play against, so I am proud of myself that I managed my emotions and played a good tie-breaker.
"I was trying to keep holding serve to stay in the second set and ended up taking the set in the tie-breaker."
Carreno Busta ended Gael Monfils's bid to win the title on home soil, the Spaniard triumphing 7-5 7-6 (10-8).
Monfils was 5-3 up in a second-set tie-break but failed to force a decider as Carreno Busta advanced for a showdown with Hurkacz.
Australia's James Duckworth is into his first ATP Tour final after beating No.8 seed Ilya Ivashka 6-3 7-6 (7-4) at the Astana Open.