Cut the peel off of the orange, making sure to remove all of the white pith. Cut out the orange slices. Save any excess juice. Cut the apples into quarters, peel, and remove the core. Cut into slices and immediately mix with lemon juice.
Peel the pineapple and cut into eighths. Remove the core and cut crosswise into slices.
Cut the melon in half, remove the seeds, and scoop into balls with a melon baller.
Bring the sugar and water to a boil in a small pot. Allow to cool until syrupy. Add the rum and the orange juice. Pour over the fruit salad. Mix the syrup with the fruit and chill for about 30 minutes. Serve garnished with red currant clusters.