Note the diacritical mark on the first e in cr pe . It is indicative of the s which followed that e in an earlier version of the French word. The s was dropped in French in the 16th century. Lam is a fabric made of silk or other threads interwoven with metallic threads. It gets its name from lame , which was a thin metal plate applied to the small overlapping steel plates used in old armor.
English cognates are lamina and laminate .
Rayon is, interestingly, named after a fairly old cognate of the English word ray . It was applied to a synthetic cloth in the early 20th century, presumably because of the cloth's sheen. While we're on synthetic materials, there's spandex , which, as you probably surmised, is simply a clever inversion of expand . Then there's tartan . This word seems to arise first in the 16th century.