That black plastic appears to be builders underlay film which prevents rising damp through the slab. I'd advise chipping off all that excess concrete so it is flush with the wall. You can then apply Crommelin Exterior Grade Brushable Waterproofer from the black plastic up over the concrete slab and then finish at the bottom of the first course of bricks. You then should install an expansion joint to isolate the new slab from the wall. Next, you'll form up your concrete path/perimeter and pour your new slabs.
You should find these step-by-step guides helpful: