In a food processor, puree honeydew, lime juice, moscato, mint, and 1/4 teaspoon salt until smooth, about 2 minutes. Transfer to a bowl, and refrigerate.
Rinse out food-processor bowl. In food processor, puree cantaloupe, creme fraiche, honey, lemon juice, and remaining 1/4 teaspoon salt until smooth, about 2 minutes. Transfer to a bowl and refrigerate. Both soups can be made 24 hours in advance.
To serve soups, divide three-fourths of the honeydew soup among four soup bowls, and divide three-fourths of the cantaloupe soup among four other soup bowls. Garnish each serving of honeydew soup with remaining cantaloupe soup, and each serving of cantaloupe soup with remaining honeydew soup. Serve immediately.