As I see it French drains come is two parts, the collection bit (where the water is) and the dumping bit (where you want the water to end up). So for the collection bit, you need open gravel to the surface so the water can get into it, even a couple of inches of top soil can stop water draining away. So this means a membrane around the gravel to stop the soil being washed into it. Then for the dumping bit, remembering that the water is going to flow out of it, needs just a bit of plastic over the top, it is unlikely that the water flow is ever going to fill the pipe. But it needs to sit on a wide bed of gravel to eases the soaking away of the water within the pipe. It is paramount that the whole system is laid on a slope, else you have built a soak away, which might cure the problem, but only accidently.
The classic French drain is just an open ditch filled with large pebbles which is a container for the water, which the pebbles help to evaporate.
Frank