Remove the stones from the peaches, and slice.
Add two of the sliced peaches to a high-powered blender. Blend until well chopped, then add the wine, and blend again until no lumps remain. At this point, you can pass the mixture through a fine mesh or muslin if you like (I didn't bother).
Add the lemonade and basil leaves, and mix well. Add the remaining peach slices, and serve over ice.