This thread is resolved. Here is a description of the problem and solution.
Problem: The HTML of the language switcher is the following:
This is not a valid HTML, consequently the screen readers read nothing. ?How can I set up a valid HTML for the language switcher.
Solution: If you desire to add the names of the languages to the language switcher, you can do so in WPML -> Languages -> Edit the language switcher (it could be in a menu, in the footer or a custom language switcher) -> Select the option to show the name of the languages and Save the changes.
This will add content to the HTML.
This is the technical support forum for WPML - the multilingual WordPress plugin.