Edmund was a set and a break up in the semi-final match at the European Open but his experienced opponent battled back to win in three sets.
Beverley’s Edmund has been in a rich vein of form of late and is closing in on a place in the world’s top 40.
The Antwerp tournament was the first time he has reached the last four of a 250-ranking point ATP event.
He beat former world No 3 David Ferrer in the second round before knocking out Andreas Seppi in the quarter-finals on Friday.
The 21-year-old carried his electric form into the last four encounter and took the first set 6-3 against Gasquet, who has reached the Wimbledon semi-finals in the past.
Edmund then broke Gasquet’s serve in the opening game of the second set and looked on course to take victory.
But Gasquet found top form and hit back with two breaks to take the second 7-5. And he continued his form into the third and decisive set where he rattled off two more breaks to win 6-2.