In a bowl, whisk together sour cream and whipping cream until smooth. Cover with plastic wrap. Let stand at room temperature until thickened (24 to 36 hours). Refrigerate the creme fraiche.
In a large saucepan, combine rhubarb and sugar. Bring to boiling over medium heat, stirring frequently until rhubarb begins to release juices; reduce heat. Cover and simmer the mixture for about 3 minutes or until rhubarb softens.
Stir in strawberries; cook, covered, about 2 minutes more or until berries are softened. Stir in blackberries; cook about 5 minutes more or until the berries fall apart. Remove pan from heat. Transfer fruit mixture to a non-metal bowl; cool. Stir in lemon juice and salt.
Remove the crust from the brioche; reserve the crust for another use. Cut the bread into 1/2-inch cubes.
In six to eight 6-ounce custard cups, spoon fruit mixture to make a 1/2-inch-deep layer. Sprinkle enough brioche cubes over fruit to form a solid layer; gently press into fruit mixture to make a more solid layer. Spoon in enough fruit to completely cover the bread cubes; sprinkle with more bread cubes and press in bread. Repeat the layers to fill the cups slightly above the rims, ending with fruit mixture. Place cups on a baking sheet. Cover with waxed paper. Refrigerate the pudding at least 8 hours or up to 24 hours.
Serve dessert with creme fraiche. Garnish with fresh berries. Makes 6 to 8 servings.