When I say break up the concrete out about 18" from the wall, this just provides you with a good wide work area...the drain pipe will go up against the foundation (or close to it)
I didn't know what kind of basement wall you have..
..cinderblock is the most common. But with 18" of stone and moisture coming up from underneath, clearly water is coming up under or through the stone footings. The French drain, as I have described, should provide a path of least resistance to channel the
water to a low corner, where you can pump it away.
Lowering your basement floor is another matter altogether. I don't recall you saying what the present floor is, but the limiting factors in how far down you can excavate is the depth of your foundation
s footings (can't go below that), the depth of your main sewer drain (you can go below that, but you will have an ugly pipe to deal with or if you run it under the new slab, you will have to install a sewage lift pump...something most people don't like to
do) and outside access (typically, you will have to break up whatever steps you have, re-excavate and put in new steps). Also, you have to extend your basement steps, HVAC ducting and plumbing to a water heater, etc.
I've done two of these floor loweri
ng projects, both came out great and gave the new owners a new living area. But planning is the key here, and understanding that it will be a lot of work.