Bring basil, sugar, peppercorns, salt and water to a boil in a small saucepan, stirring to dissolve the 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, kiwi and grapefruit in a large bowl; pour syrup and accumulated juices over fruit, and gently toss. Let stand and room temperature, stirring occasionally, for at least 30 minutes and up to 2 hours before serving.