Put 6-8 champagne glasses in the freezer to chill for at least 2 hours. Soften the gelatine leaves in a bowl of cold water for a couple of minutes, then drain.
Open the bottle of champagne and pour about 75ml into a small pan. Immediately seal the bottle.
Gently heat the champagne in the pan with the sugar and Crème de Pêche, and then add the softened gelatine leaves. Do not let the liquid boil. As soon as everything has dissolved, remove the pan from the heat and skim off any scum that has risen to the surface.
Remove the glasses from the freezer and divide the gelatine mix between them. Tilt each glass and pout the remaining champagne in a dribble down the inside of the glasses, so that you minimise the froth and maximise the bubbles.
Return the glasses to the freezer for an hour to set, then store in a fridge until ready to serve.