Using a stainless-steel knife, cut melons in half, creating a sawtooth edge. Scoop out seeds and stringy fibers. Using a melon baller, scoop flesh from melons. Place melon balls in a large bowl, and sprinkle with sugar. Add wine, lemon juice, and basil. Cover with plastic wrap, and transfer to refrigerator to macerate for 2 hours. Scrape remaining melon from shells until smooth, creating bowls. Cover with plastic wrap, and refrigerate until ready to use.
Spoon macerated melon balls into shells. Top with strawberries and raspberries. Garnish with mint, and serve immediately.