Place cubed watermelon and sugar in the pitcher of a blender. Blend for 1 minute. Stir in the champagne. Pour the watermelon mixture into a plastic container, cover and place in the freezer. Stir the mixture with a fork every 30 minutes until frozen, about 2 hours.
Before serving, remove the frozen granita from the freezer and stir well using a fork or place in the food processor and process until it reaches the desired consistency. Serve in tall glasses garnished with sliced watermelon.