Is it okay to insulate a basement wall when an interior french drain is installed?
Just noticed this question was never answered, but I did wind up closing everything up later that year and never had any issues. I sold the house earlier this summer (2020).
I figured that, if rigid foam insulation was acceptable, then any kind of moisture barrier would be, too. The rough texture of the cinder blocks and mortar joints would allow for at least some air movement, and worst-case, any mold that might happen to form would be trapped behind the moisture barrier.
So I covered the wall in the thickest plastic sheeting I could buy. I stapled it to the sill plate at the top to keep it in place, then tucked the bottom edge into the flashing for the interior French drain. Any water that comes through the brick wall now hits the backside of the plastic sheeting and runs into the interior French drain.
Once that was done, everything else was generally finished as pictured in my question. I used pressure treated lumber, ripped it into furring strips, used concrete anchors to attach them to the wall, removed the vapor barrier from the fiberglass insulation (to allow the wall cavity to breathe into the room, because the plastic sheeting is a vapor barrier to the exterior, insulated the cavities, then drywalled over everything.
I did everything on the up-and-up so, while I'd bet someone has something to say with how this was done, it passed framing, insulation, electrical, and finish inspections, and the house passed the home inspection when I sold it.