Heat the sugar with 450 ml of water in a saucepan, stirring until the crystals are dissolved, then let the syrup bubble gently for 5 min. Remove from the heat, cool and refrigerate.
Remove the skin from the peaches. (For unruly fruits, first pour boiling water over them and then quench). Cut the peeled fruit in half. Remove the stone from each. Roughly chop the flesh. Squeeze lime, pour juice through a sieve to the peach pulp. Blend both together in a hand blender. Add the cold sugar syrup and chill in the refrigerator.
Pour the sorbet pudding into the ice cream maker and freeze.
Transfer the soft sorbet to a large enough bowl and place in the freezer for about half an hour to firm up.
Shape sorbet into balls with a portioner, fill into wide glasses, top with chilled sparkling wine and bring to the table on the spot.
Tip: Pre-chill the baking dish for the sorbet and the wide serving glasses in the freezer.