I meant to say that you could definitely use a patchwork piece made of quilting cotton for the above design (in the middle part), but you probably could not use a layered and quilted piece unless you made the quilted part only as wide as the part that shows and left the top just enough wider to tuck in, if that makes sense. That could work okay, probably. You can change the fabric later if you don't use glue. These came in different styles. I googled just now and found the website of a company that makes them.
http://www.cornicekits.com/index.php?page=cornice.inc They sell expansion kits to make them wide enough for a bigger window, and if your window is smaller, there are instructions for cutting them to size.
Also, Joann's has some made by June Tailor, but I don't know how they compare.