French doors can be really tricky to dress up with window treatments, because it's not the same thing as dressing up a regular window. This is a window, but you have to be able to get in and out of at the same time, so functionality is the most important thing. So you either want the window treatments directly on the door or you want them around the door.
If you're putting them around the door, all you need to do is put a rod right across the upper portion of the door, maybe a couple of inches above, and then do panels on either side of the door. Then it won't get in the way when you're going in and out. You can also achieve this look by using what's called a hold back. They're round little attachments to the wall, and basically you're looping the loops of your curtain on each one, and it gets a little bit more decorative.
Now if that gets a little crazy or you want a layer effect, you can do what's called a shirred curtain on the door itself. What's great about this is that they're two rods, one above the opening of the door, which is the window portion and one at the very bottom.
This will cover your windows, so that you have the privacy that you need, but it won't swing around when you're opening and closing the door. The two rods help stabilize the curtain and so you get the privacy. The shirring of the curtain makes it decorative, and then if you want to go that extra step measure, you can do the window treatment around the door, as well.