Prepare the peaches. If using fresh peaches, wash, peel if desired, and slice them into even pieces. If using frozen peaches, let them sit for 2 to 3 minutes so they soften slightly for easier blending.
Blend the fruit base. Add the peach slices, lemon juice, honey or simple syrup, and white grape juice to a blender. Blend for 30 to 45 seconds until the mixture is smooth, thick, and silky. If it looks too thick, add 1 to 2 tablespoons of extra juice.
Taste and adjust. Taste the peach puree and add a little more sweetener if needed. The flavor should be bright, peachy, and slightly tangy.
Fill the glasses. Spoon or pour the peach mixture evenly into 4 glasses, filling each about halfway. Add a few ice cubes if you want the drinks extra cold.
Top with bubbles. Slowly pour the chilled sparkling water or non-alcoholic sparkling cider into each glass. Pour gently so the fizz stays lively and the drink keeps its pretty layered effect.
Stir lightly and garnish. Give each drink a gentle stir with a long spoon. Garnish with fresh peach slices and mint leaves.