Combine first 3 ingredients in a small saucepan; bring to a boil.
Remove from heat; cool to room temperature. Strain rosemary syrup in a sieve over a bowl; discard solids. Cover and chill at least 1 hour.
Place rosemary syrup and peaches in a blender, and process until smooth. Strain mixture through a sieve over a bowl; cover and chill at least 4 hours. Spoon about 2 tablespoons peach syrup into each of 8 Champagne flutes, and top each serving with about 1/3 cup Champagne.
