Bring a medium saucepan of water to a boil. Add peaches and simmer for about 2-3 minutes. Transfer peaches to a bowl of ice water. The peel should now be easy to remove by rubbing gently with a dry paper towel. If not, remove skin with a paring knife or vegetable peeler. Remove peach pits and cut into cubes.
Add peaches, lemon juice and sugar to a food processor. Process peaches until you have a smooth puree. Refrigerate until ready to use or make into sorbet (see below)
Distribute peach puree or sorbet (see below) among 4 champagne flutes or wine glasses. Top with sparkling wine, and stir gently.
Sorbet (optional)
Spread puree onto a baking sheet lined with waxed paper. Place in the freezer until frozen. Break up frozen puree into chunks, and return it to the food processor. Process until it forms a thick sorbet, scraping down the sides as needed.
Notes
You may need more sugar depending on the sweetness of your peaches. Taste the puree after adding 1 Tablespoon. If it tastes very sour, add more, 1 teaspoon at a time until you reach your desired sweetness.