I don't think there is any way to mount them without the hardware showing. Even if you could it would require screwing into the door and if it is not a solid wood door it wouldn't hold very well. You would also have the problem of the blinds banging against the glass when opening and closing the doors.

I think I would prefer drapes on a rod mounted above the door. However the choice is yours. I'm just pointing out the pitfalls. Good luck whatever you decide.

I don't think I've ever seen a french door that the wooden parts of it weren't solid wood. So, I don't think having a solid surface to mount hardware will be a problem. Oilpainter is right that the shade will bang when it's opened or closed. Only you can decide if this is a major drawback. Go check out mounting hardware to see how the different styles are mounted and how the shade has to be constructed to conform to a mounting style that suits you. There is something out there for almost anything you want to do. Believe me. You're not the only one to ever have this problem.

Unless the door is opened and closed a million times a day, I would much rather have a banging shade to a drape that impedes the door opening or that would have to be drawn or pulled back to use the door.

I made roman shades for my french doors and installed them as follows:

1. Sew velcro at the top of shade and also to the valance.
2. Mount shade on a 1x2 board with the shade stapled to the 2" side so that the projection is the 1" side.
3. Screw the 1x2 mounted shade into the wooden door at least 1" above the glass so that you don't inadvertantly break it. Use screws with heads that will be flat against velcro or fabric.
4. Install valance to cover screws.

I used a self locking cord lock so I don't have a cord cleat. When the shade is raised, I simply stuff the cord into a fold to hide it. The shade lays perfectly flat against the door and doesn't bang on the door at all.

Good luck!