Mensik followed up his quarter-final win over fifth-ranked Andrey Rublev (26) by seeing off Monfils 6-4, 1-6, 6-3.
At 18 years and five months, Mensik is the fifth youngest ATP finalist since 2005 and the youngest since Alcaraz went to the Umag championship match in 2021.
Mensik, who will rise from 116 in the world to inside the top 100 next week, will take on Karen Khachanov (27) in Saturday's final.
"It's amazing. It's been an incredible week so far," said Mensik who has also defeated former world number one and three-time major winner Andy Murray (36) in Doha.
The Qatar Open is just his third main draw event following breakout runs to the third round of the 2023 US Open and a second-round appearance at the Australian Open last month.
"Gael played unbelievable. I know it is tough to play against him, especially with his good movement. For me every point I have to play my best game," said Mensik.
"I have to say this performance was one of the best in my entire life. I am so glad I reached this level in the semis, so hopefully tomorrow I play like this. An amazing feeling with my first ATP final.
"I am speechless."
Monfils was the Doha champion in 2018. Mensik was not even born when the crowd-pleasing French player made his maiden appearance at the tournament in 2005.
"Gael is one of the biggest showmen on court. He is a great guy. The rallies were so fun with him," added Mensik who saved nine of 12 break points patiently carved out by Monfils.
Russian second seed Khachanov defeated Australia's Alexei Popyrin (24) 7-6(12), 6-2 in his semi-final.
Khachanov will be chasing his sixth tour-level title on Saturday.
