Just in case, I finally found some kind of answer. So, if any French speaking people are looking for the right kind of fabric, it seems that it is "velours de coton".

Hello everyone. I'm looking for the right fabric to make a AOTC or ROTJ Royal Guard. But since I'm living in Quebec and French is my mothertongue, the translation of the CRL are a bit touchy. "The outer robe is constructed of crimson red velvet or velveteen. Velour, crushed or panne velvet are ...