What kind of edging should I use between a patio and a French drain?
Here is an idea that might work for you...


Here is a revised drawing added to the first one, with the idea you had given to you and I added where the various barriers need to be.


I forgot to note in the drawing that the gray line is the filter cloth.

The full wrap of the plastic membrane will keep the excess water from migrating back to the house. Just placing it against the wall and the bottom will allow it to get to the walls still. Remember it will be a LOT of water concentrated there. 

The plastic liner will act as an in ground gutter to move the water, so be sure the bottom is accurately graded towards a place the water can flow that will do the house no harm.