Sauce: Combine Champagne, shallots, vinegar, and peppercorns in medium saucepan. Simmer until reduced to 1/4 cup. Can be made 8 hours ahead. Cover and let stand at room temperature.
Shrimp: Combine Champagne, olive oil, shallots, and ground pepper in ziplock bag- Add shrimp and seal; make sure that shrimp are coated evenly. Marinate shrimp at room temperature for 30 minutes, turning bag occasionally. Mix chives, tarragon, and parsley in small bowl.
Preheat oven to 400 degrees. Spray baking sheet with nonstick vegetable oil spray. Drain shrimp and arrange on prepared pan in single layer. Bake for 5 to 8 minutes or until just opaque. Arrange on plate.
Rewarm sauce base over medium-low heat. Whisk in butter 1 piece at a time, allowing each to just melt before adding next (do not boil or sauce will separate). Season beurre blanc to taste with salt and pepper.
Spoon warm sauce over shrimp and serve.