Cook peaches, sugar, and 1/2 cup water in a medium saucepan over low heat until mixture is very hot and peaches have softened, about 15 minutes. Stir in corn syrup and lemon juice. Remove from heat.
Purée until smooth using an immersion blender (or use a regular blender, working in batches). Pour peach purée through a strainer into a bowl, using a ladle to push purée through. Chill mixture until cold.
Make sorbet: Add 1 cup sparkling wine to peach purée (cork remaining wine and chill until ready to serve), then freeze in an ice cream maker according to manufacturer's directions. Transfer to a sealable container and freeze until firm, about 5 hours.
Make Bellini: Pour 1/4 cup reserved sparkling wine into each of 8 chilled Champagne flutes, then top with 3 small scoops of sorbet.