If using fresh peaches, remove the pit from all 3 peaches. Dice 2 of the peaches and add to the bowl of a food processor. Add the sugar and puree until smooth, then press through a fine mesh sieve. Chill until ready to use.
Thinly slice the remaining peach.
Place 1 to 2 tablespoons of peach puree into each of 4 champagne flutes. Top the glasses with prosecco and drop in a peach slice before serving.