Keeping the skin on the peaches, carefully cut each peach away from the pit (seed). Slice the peaches into fairly thick slices (about 1/2-inch thick).
To a medium size bowl, add the sliced peaches, lemon juice, sugar, salt, cinnamon and corn starch. Gently mix together until the peaches are coated.
To the bowl, add blackberries. The blackberries are added last so that they don't get mashed or broken up when mixing the filling ingredients. Set aside.