cosmetic is usually an adjective.
cosmetics is always a noun. It can be used in the singular, in specific instances: Lipstick is a cosmetic.
Since cosmetics can be used in the singular and still be a noun, then either "the cosmetic industry" or the "cosmetics industry" is accurate, although the latter is probably preferred, as we're not speaking of a singular lipstick industry here.
I don't think we want to use "cosmetic" as an adjective here, as that would mean we are describing the industry as serving to beautify or as superficial. So it seems a compound noun works better.
I try to think of substitute situations to determine what is right and wrong. In this case, I thought of the sheep industry. Sheep is a plural or singular noun. The adjective is sheepish, or sheeplike. You wouldn't say the industry is a sheepish industry. Nor is their product a woolen industry.