Bring basil, sugar, peppercorns, salt, and water to a boil in a small saucepan, stirring to dissolve sugar; boil 1 minute. Remove from heat, and let cool. Pour syrup through a fine sieve into a bowl; discard solids.
Working over a bowl, cut segments of grapefruits free of membranes. Combine pineapple, kiwifruit, and grapefruit in a large bowl; pour syrup and accumulated juices over fruit, and gently toss. Let stand at room temperature, stirring occasionally, at least 30 minutes and up to 2 hours, before serving. Fruit can be combined 1 day ahead and refrigerated. Thirty minutes before serving, remove from refrigerator, and toss with syrup.