The word fabric refers to any sheet of material made by weaving things together. This means that chainmaille is a fabric while paper is not. (of course, by this definition, felt isn't a fabric either)
So period fabric materials included:
- Linen - mainly for underclothes and lining wool
- Cotton - rare in late period, almost completely non-existant in early period, generally a fluffy fabric like flannelette, not often similar to our modern cotton
- Wool - used for dresses, tunics, cloaks
- Silk - expensive because it was brighter, stronger, and nicer.
- Hemp - used by peasants sometimes in place of linen. Hemp is coarser than linen.
- nettle cloth - yes early period people made cloth from nettles, I think it was somewhat like linen.