Put sugar and Champagne in a medium heavy-based pan and stir over a low heat until sugar is dissolved and mixture comes slowly to the boil. Cook for 2-3 minutes, then remove from heat and pour champagne syrup into a bowl. Let cool, then cover and refrigerate.
Process watermelon and strawberry in a food processor until smooth. Put mixture in a fine strainer over a bowl and push mixture through strainer using a wooden spoon. Discard pulp. Pour strained mixture into cold champagne syrup and stir to combine. Pour into a shallow cake tin, cover with plastic wrap and freeze for 4-6 hours. Stir granita with a fork every hour to break up ice crystals until set.
Remove granita from freezer and refrigerate for 10 minutes. Spoon granita evenly between 6 champagne glasses, then pour over extra Champagne and serve immediately.