The British number three had been bidding to reach his first final on the ATP Tour, but Pouille came from behind to claim a 6-7 6-4 6-3 win.
Edmund created six break-point opportunities during the opening set but although Pouille had two set points during the tie-break, the 22-year-old saved them both before establishing an advantage.
However, Edmund dropped serve in the first game of the second set and that was enough to allow his French opponent to take the contest into a decider.
Pouille's serve was improving by the set and as he conceded just one point behind his delivery in the third, Edmund dropped serve twice to miss out on a showdown with Jo-Wilfried Tsonga.
The two players are in for a quick reunion, with the pair having been drawn against each other in the first round of next week's Paris Masters.