In a medium saucepan, bring peaches, sugar, and 1 cup water to a boil over medium-high heat. Reduce heat to low, and simmer for 5 minutes. Let cool slightly. Transfer peach mixture to the container of a blender; purée until smooth.

In a large pitcher, stir together peach purée, sparkling water, lemon juice, and mint. Top with ice. Garnish with mint sprigs, if desired.