Combine water, sugar, torn mint leaves, and torn basil leaves in a saucepan. Boil over medium-high heat until sugar dissolves. Cool and stir in corn syrup. Pour cooled sugar syrup through a sieve; discard solids.
Place 2 cantaloupe balls and 2 honeydew balls in each ice pop mold. Combine 1 cup sugar syrup and Champagne. Divide Champagne mixture among ice pop molds. Cover and insert craft sticks; freeze 4 hours or until thoroughly frozen.