Fix the output of the XML sitemap so they show the correct localised URLs. This is an add-on for when you change the URLs using other techniques.
With WPML you can localize the slug of your CPT single, but not your CPT archive, if you give it a different content. You can fix the translations with https://gist.github.com/rmpel/d9989da79956fb0eafe81e49331b84b6 .
With WPML you can localize the "page for posts", but this will not localize the post-URL-base. You can fix this with https://gist.github.com/rmpel/5672b2b943a4a015fe1777c0a31fac59 .