First, make simple syrup; combine sugar and water in a medium size heavy saucepan and bring to a full boil. After six minutes, remove from heat and add champagne, lemon juice and lemon rind. Allow to cool, then pour into a shallow dish and place in freezer.
When mixture is partially frozen and mushy, beat with a whisk or fork until smooth, then return to freezer. Repeat this procedure two more times before transferring sherbet to a covered container and allowing it to freeze completely.