The Argentinian – who knocked out top seed John Isner in the quarter-finals – claimed another big scalp on Friday at the ATP 250 event.
Delbonis needed just 70 minutes to set up a showdown with Ernests Gulbis as he posted a 6-2 6-4 victory.
Fourth seed Simon was sloppy on serve throughout the contest and that allowed Delbonis to claim 11 break points.
He converted four of them – two in each set – and served well himself in an impressive performance.
The world number 45 won 27 of 33 points on his first serve as his continued his good run on clay ahead of the French Open.
Delbonis will meet Serbian Dusan Lajovic in the first round at Roland Garros after Friday's draw was announced.
Second seed Gulbis is sure to present a tough challenge for Delbonis, though, after he thrashed defending champion Albert Montanes of Spain 6-0 6-3.
Latvian Gulbis won all but one of his 27 points on first serve in a dominant performance that also saw him claim five breaks.
Gulbis – who is seeded 18th for the French Open and begins with a clash against Lukasz Kubot - has never played Delbonis before.