Bring sugar and water to a boil in a small saucepan, stirring until sugar has dissolved, then transfer to a bowl and cool syrup completely (or quick-chill by setting bowl in an ice bath and stirring occasionally until cool). DO AHEAD: Syrup can be chilled up to 1 week.
Stir together juices, wine, Cognac, mint, fruit, and cooled syrup in a large pitcher. Chill, covered, until cold, about 1 hour. Stir in Champagne. DO AHEAD: Punch, without Champagne, can be made 3 hours ahead and chilled, covered. Add Champagne just before serving.
