1. Stir sugar and brandy in medium bowl. Crush about 10 blackberries; add to brandy mixture. Let stand 1 hour at room temperature, then strain. (Can be prepared 1 day ahead. Cover; chill brandy mixture and remaining blackberries separately.)
2. Divide brandy mixture among 6 Champagne glasses. Add 2 blackberries to each glass. Fill halfway with Framboise and the rest of the way with Champagne; serve.