Combine sugar and wine in small saucepan; bring to a simmer. Remove from heat. Add 3 basil sprigs and orange zest; stir to immerse. Cover and let steep for 30 minutes.
Strain syrup into a small bowl, pressing on basil and zest to release maximum flavor.
Shortly before serving, combine peaches, blackberries, lemon juice and basil-infused syrup in a serving bowl; toss gently to coat. Serve garnished with basil sprigs.
To peel peaches, dip in boiling water for 30 or 40 seconds to loosen their skins. Let cool slightly, then slip off skins with a paring knife.