Pink Grapefruit Champagne Sorbet with Pink Grapefruit Sauce

Stir first 4 ingredients in large saucepan over medium heat just until sugar dissolves. Strain into bowl, pressing on solids; mix in Champagne. Pour 2 cups juice mixture into medium saucepan. Refrigerate remaining juice mixture in bowl. Simmer mixture in saucepan until reduced to 3/4 cup, stirring occasionally, about 25 minutes. Refrigerate reduced mixture to use as sauce. Transfer juice mixture in bowl to ice cream maker and freeze according to manufacturer's instructions. Transfer sorbet to container; cover and freeze. (Sauce and sorbet can be prepared 3 days ahead.)Cut peel and white pith from grapefruits. Working over bowl, cut between membranes to release segments. (Can be prepared 6 hour ahead. Place segments in bowl with juice. Cover and refrigerate.)Chill 6 plates in freezer. Scoop 3 ovals of sorbet onto each plate. Spoon sauce around sorbet. Decorate with grapefruit segments. Garnish with mint.