Combine all 6 ingredients in a small saucepan and bring to a simmer. Stir occasionally until the cranberries burst and release their juices, about 5 minutes.
Remove the syrup from the heat and let steep for 15 minutes. Strain into a glass jar, pressing gently on the cranberries to extract their juices. Transfer the syrup to the refrigerator to cool completely.
Fill a Champagne flute with 1 ounce cranberry-rosemary syrup. Layer with ½ ounce orange juice, and top with 6 ounces Champagne. Garnish with an orange slice, a few cranberries and a sprig of fresh rosemary.
Repeat with the remaining cocktails and enjoy!