Wash the limes and grate them dry. Finely grate the zest of 5 limes and squeeze the juice. Mix the juice with the peel and 500 ml of water and pour into ice cube containers. Freeze for about 4 hours.
Peel and halve the melon and scrape out the seeds with a spoon. Cut the melon into small cubes. Cut the remaining limes into thin slices. Put lime slices in a large bowl, sprinkle with sugar and crush a little. Add melon and mix with cachaça. Put the punch in a cool place for about 3 hours.
Just before serving, remove the ice cubes from the moulds and add them to the punch. Pour in mineral water and champagne. Decorate with mint and serve.