I'm not sure about EU laws specifically, but as far as I know merchants can definitely discriminate between credit card issuers.
I also do not see any official way to have AMEX contact a merchant to try and get their cards accepted. The best way to get that changed is to simply tell the merchant (at checkout or in some "tell us how we did" review).
The biggest reason why AMEX is not accepted is because of the fees involved. Visa and Mastercard charge the merchant about 1.5% to 2.5% per swipe (or "insert chip" nowadays), whereas AMEX can charge up to 3.5% or more. Merchants simply don't want to pay that much.
Years ago AMEX was a "premium" credit card (higher limits and more perks, usually used by big spenders) but has since become more mainstream.