I have the same problem. With The Events Calendar plugin active, I’m not able to link languages between pages or posts, or even assign a language when saving.
However, if I comment this line (line 2937 in “/plugins/the-events-calendar/lib/the-events-calendar.class.php”) it works fine:
remove_action( 'save_post', array( $this, 'addEventMeta' ), 15, 2 );
I don’t know what to do. Using another calendar plugin is not an option in this particular case, and commenting that line doesn’t seem a very good solution.