Combine sugar and 3/4 cup water in a small saucepan over medium-high heat. Cook 2 minutes or until sugar dissolves, stirring constantly. Remove from heat; cool completely.
Combine sugar mixture, juices, Chambord, vodka, and food coloring, if desired, in a large bowl; stir well. Pour mixture into the freezer can of an ice-cream freezer; freeze according to manufacturer's instructions. Spoon sorbet into a freezer-safe container; cover and freeze 8 hours or overnight.
I was so disappointed in this recipe! A French martini is one of my favorite drinks, so I was very excited about the frozen dessert version. It's awful! Even with the unsweetened pineapple juice, it's so sweet, I think it would send a Clydesdale into sugar shock!