The French stitch is a stitch that runs to the left of the seam and a stitch that runs to the right of the seam. I'm going to do French stitching on my truck interior, which I am doing myself, this year.
Contrary to popular belief, it really doesn't produce a stronger seam ... necessarily. That additional material you mention, RESTOMAN57 (as I'm sure you know) is called twill -- I was recently told that twill is not cut on the bias and therefore has *no* stretch or give to it. It doesn't take much to figure out what that will do; the French stitches, at each side of the twill, are going to take all the abuse! The leather or vinyl has give; the twill does not.
A trimmer I know uses headliner thingies (I forget what it's called but it's like twill only it's cut on the bias, so it gives, and is used to hang the old headliners that are hung by bars) ... he also tells me that most trimmers he knows don't use any backing at all when they do French stitching because the seams hold up better than they do with the unforgiving twill applied.
Note: I'm just learning, so I'm no expert but this is what I've learned from those who are the experts.