The sixth seed Shelton defeated seventh-seeded Fils 6-3 7-6 (11-9) in the semi-final after recovering from 6-3 down in the second-set tiebreak on Saturday.
"I served really well, and I had to because I know what Arthur is capable of," Shelton said on court.
"The goal was to let him know I got clean hits on the ball as much as possible, and I executed really well. I'm not sure how I pulled that tiebreak out in the second set."
Fils won their quarter-final in Tokyo a month ago, but Shelton's run this week has guaranteed the American's return to the top 20 from No.23 when the rankings are updated on Monday.
Mpetshi Perricard is set to improve his career-high 37 after reaching his second final of a breakthrough year.
The unseeded 21-year-old Mpetshi Perricard upset No 4 seed Holger Rune 7-6 (8-6) 6-4 by serving 17 aces and has yet to lose serve in Basel.
"Inside of me there was a lot of emotion, but I tried to calm it down," he said. "It's nice to be in the final and I hope to get the win."
Mpetshi Perricard started the year ranked 200, won a bunch of Challenger titles, and then graduated to his first ATP-level title in Lyon in May. He'll be able to take confidence from having beaten Shelton in their only previous meeting in June on grass at Queen's Club.
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