The 19-year-old from Westmount, Que., was edged 7-5, 6-7 (5), 6-3 by third-seeded Alize Cornet of France.
Cornet broke Bouchard twice in the last set and saved six break points in the three-hour match.
Cornet will take on last year's runner-up Lucie Hradecka in Saturday's final. Hradecka of the Czech Republic rallied to beat Italian qualifier Flavia Pennetta 1-6, 6-3, 6-1 in Friday's other semifinal.
The Strasbourg tournament is a warm-up event for the French Open, and Bouchard will face Tsvetana Pironkova of Bulgaria at Rolland Garros in the opening round, the first match of her young career in the main draw of a Grand Slam.