Pour wine into a 23x33 centimeter baking pan and place in the freezer for eight hours.
Combine sugar, water and basil leaves in a small saucepan and simmer over medium heat until the sugar has dissolved, approximately two to three minutes. Transfer to a heat-proof bowl or jar and place in fridge to cool completely.
Scrape the frozen wine into a blender. Remove basil leaves from mixture and add syrup to the blender with watermelon, lime juice, and ice. Purée until smooth.
Serve immediately, garnished with watermelon and basil or place blender into freezer for up to 30 minutes at a time, blending after each period and before serving.