Muslin, might be an option. I'd say canvas a light one, could work. I do like paper as it looks good and is easily thrown away when dirty.
Photography
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saying that it is fabric is too generic. the properties of fabric are not the same across the several different types. I would assume that you are talking about muslin. Canvas has different qualities. As does polyester. All are used for backdrops.
You are probably looking for fleece-backed polyester like the Titanium cloth from Backdrop Outlet. This is not an endorsement for them. I have several of them, but they (BDO) are a pain to deal with in ordering and customer service. They travel well. They do drape somewhat. And they can be laundered. They have a some spring to them so you can tension them with clamps and sandbags to pull out wrinkles.