Don't use fabric. Go into a JoAnn's and snoop around in the upholstery and drapery departments for something that might be a reinforcing mesh for formal valances and stuff. Shop with your hands; you'll know the right texture when you touch it.
Fay's suggestion of iron-on interfacing might be the best way to attach your mesh to a more continuous fabric.
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Fay's suggestion of iron-on interfacing might be the best way to attach your mesh to a more continuous fabric.