For the syrup, bring sugar and 1⁄4 l water to the boil in a pot and boil down over medium heat for about 10 minutes until syrupy. Stir frequently, then let it cool down.
Carve peaches crosswise, pour hot water over them, rinse cold and skin them. Halve the fruit, remove stone, puree flesh. Mix with syrup, champagne and lemon juice. Pour into an empty, clean ice container.
Cover and freeze for about 6 hours, stirring the mixture more often with a fork.