I would consider leaving the brick chunks, they'll drain well. You can just put whatever you want as the run base on top of them. French draining is a perforated pipe which helps transport water away from an area. Look it up on wikipedia.
The way I built my run, was that I put down perforated tubing on the bottom on top of the solid rock that we have under our yard, then I took coarse gravel (about 15-30mm) on top of the pipes in about an 20-30cm layer. On this I put down some hardware cloth to keep rats and other critters from burrowing into the run. Then I put down sand on top of that to form the base of the run, that layer is about 10cm for me but could be deeper. Right now in the summer we throw grass clippings and garden waste in there and rake it away about once a week. For the winter, I'm planning on bagging up dry leaves and pine needles and starting a deep litter in the run.
The way I built my run, was that I put down perforated tubing on the bottom on top of the solid rock that we have under our yard, then I took coarse gravel (about 15-30mm) on top of the pipes in about an 20-30cm layer. On this I put down some hardware cloth to keep rats and other critters from burrowing into the run. Then I put down sand on top of that to form the base of the run, that layer is about 10cm for me but could be deeper. Right now in the summer we throw grass clippings and garden waste in there and rake it away about once a week. For the winter, I'm planning on bagging up dry leaves and pine needles and starting a deep litter in the run.