Thaw peaches at room temperature but do not drain. Place peaches and their juice in a blender or food processor. Add sugar. Cover and blend or process until smooth. Transfer pureed peaches to a 2-quart pitcher. Stir in orange juice and lemon juice. If desired, cover and chill for up to 24 hours.
Before serving, slowly pour Prosecco into peach mixture; stir gently. Serve in glasses over ice. If desired, drizzle with a little grenadine syrup.