Place blackcurrants in a pan with caster sugar and water. Bring to the boil and keep over low heat for 5 minutes. Press mixture through a sieve. Leave to cool and chill for 2 hours.
Transfer mixture to a shallow container. Cover and freeze until half frozen around edges, about an hour. Whizz to a thick slush and continue freezing. Repeat whizzing process 3 or 4 times at 35-45 minute intervals until smooth; cover and freeze until set.
To serve, chill Champagne. Remove ice from freezer 10/20 minutes before serving depending how hard, and place at bottom of each glass. Top with Champagne.