Place the pineapple in a medium saucepan, then add 2 half-pints of raspberries, all the blueberries, the sugar, and 3/4 cup water in a saucepan and bring to a boil. Lower the heat and cook uncovered over medium-low heat, stirring occasionally, for 5 to 7 minutes. The juice will become a syrup and the berries will be slightly cooked. Off the heat, stir in the remaining half-pint of raspberries and the framboise, if desired. Set aside until warm.
Place about 3/4 cup of fruit in each bowl and top with a scoop of ice cream.