Melt butter in a large nonstick skillet over medium-high heat. Add onion and garlic; sauté 2 minutes or until onion begins to brown. Add mushrooms, salt, and pepper; cook 3 minutes or until liquid evaporates and mushrooms are tender, stirring frequently. Add wine, and cook 3 minutes or until liquid almost evaporates, stirring frequently. Add broth and fresh thyme; cook 2 minutes. Remove from heat; add crème fraîche, stirring until well blended. Add chicken, tossing to coat.
Place 1 crepe on each of 6 plates. Spoon about 1/3 cup mushroom mixture into center of each crepe; roll up. Garnish with thyme sprigs, if desired. Serve immediately.