Combine Champagne, peaches, salt, large sprigs of mint, and white pepper in a large saucepan or deep pot. Cook for 20 minutes over medium heat to infuse flavors. Remove from heat and remove large mint sprigs. Adjust salt and white pepper, if needed. Blend with an immersion blender and chill. Serve in demitasse cups garnished with 1/2 teaspoon creme fraiche and small mint sprigs.