Bring sugar and 1-1/2 cups water to boiling in saucepan. Reduce heat; simmer 6 minutes. Let cool.
Puree blackberries and blueberries in food processor (do not use blender). Strain through fine-mesh sieve into bowl, forcing through with rubber spatula; discard solids. Stir in lime juice.
Stir into puree the sugar syrup, cream and salt. Pour into 13 x 9 x 2-inch baking pan. Freeze 2 hours. Spoon into processor. Pulse to break up; don't over process. Refreeze 2 hours. Pulse again in processor. Refreeze until firm. Garnish.