Tsitsipas, meanwhile, is now unlikely to make it to the ATP Finals in Turin, currently at No 12 in the Race and almost 850 points behind Andrey Rublev, who stands No 8.
Fils, ranked No 20, will play the winner of the match between Russian Andrey Rublev, the top seed, and American Ben Shelton, the No 6 seed, next.
Ahead of his victory, the 20-year-old Frenchman defeated German qualifier Daniel Altmaier (7-6 (5), 6-3) and Spaniard Pedro Martinez Portero (7-5, 6-3).
Tsitsipas, ranked No 11, edged out Argentinian Francisco Cerundolo (6-3, 6-7 (3), 7-6 (4)) and won against Dutch qualifier Botic van de Zandschulp (7-6 (3), 7-5) earlier in the tournament.
Basel ATP 500, other last 8 results (St. Jakobshalle., hard, EUR 2.385.100, most recent results first):
- Giovanni Mpetshi Perricard vs. Denis Shapovalov
- David Goffin vs. Holger Rune
- Andrey Rublev vs. Ben Shelton