Bring sugar, honey and 1/4 litre of water to the boil and simmer for about 5 minutes. Let the syrup cool down. Wash the melons, cut them in a zigzag pattern towards the middle and cut them in half. Scrape out the seeds.
Remove the flesh of the netted melon from the halves up to an approx. 1 cm wide edge (keep the skins). Cut a part of the flesh into narrow slices. Puree the rest. Wash the limes hot.
Grate the skin thinly and squeeze the juice. Mix cold syrup, melon puree, lime zest and juice. Pour into a bowl and freeze for about 5 hours. Stir vigorously every 30 minutes.
Cut out small balls (or cubes) from the Charantais melon. Keep the peels as well. Marinate the balls with brandy. Scrape sorbet into curls. Arrange with 2/3 of the melon balls in the fruit peel.
Halves may be arranged on crushed ice. Serve immediately, decorated with slices of lime, mint and other melon slices and balls.