For a playful presentation, use a melon baller to scoop the fruit into bobbing orbs.
Combine rosé, liqueur, 1 mint sprig, and 1 cup each melon in a pitcher. Cover; chill at least 8 hours.
Place remaining melon in a single layer in a small baking dish; cover and freeze.
Remove mint sprig from pitcher, and discard. Stir remaining mint sprig, frozen melon, and club soda into sangria just before serving.