Add the peaches, mint leaves, honey, and 1/2 cup of sparkling water to a blender. Blend until smooth.
Transfer to a strainer lined with cheesecloth and strain the peach mixture into a bowl. You may have to sqeeze some of the liquid out as the mixture will be thick.
In an ice-filled glass, pour about 4 ounces of wine over and add the peach mixture. Top with sparkling water and garnish with peach slices and mint.