Foundation Question

Have a peculiar situation with my basement. The house when originally built in 1950 had a crawl space basement. During the 1950's the basement was dug out to obtain more height. My understanding after speaking with foundation people, is that a cement pony wall was poured and this acts as the foundation. So my understanding is that I have the original foundation on its footing and then a pony wall and a concrete slab. I have water problems and would like to install a French drain. Complications are that the area I live in is sits on a lot of rock. I have also been told that the pony wall surface facing the outside may not be smooth and straight.

My question is are there risks in digging out around the house to install a French drain in this situation. I know that it will be quite expensive, but besides costs, are there any risks related to the structure itself. I have included a couple of pictures to help you visualize what I am referring to. Thanks.

Roberto in Montreal