Cook and stir water, sugar, honey, and lemon juice together in a saucepan over medium heat until sugar is dissolved and mixture is clear, about 10 minutes.
Reduce heat to medium-low, add cantaloupe and chopped mint, and cook until liquid reduces by half, 5 to 10 minutes.
Transfer cantaloupe mixture to a wide, shallow dish and refrigerate to cool completely.
Blend the cantaloupe mixture until smooth. Stir champagne into the pureed mixture until smooth. Strain the mixture through a fine-mesh sieve onto a rimmed baking sheet.
Freeze strained mixture until completely firm. Scrape frozen puree from sheet and blend in a blender until smooth. Pour onto the sheet and freeze again until firm. Repeat process until the mixture is smooth and creamy, like a sorbet. Garnish with mint leaves.