Thank you, this is exactly what I was looking for!
Our public website is in german language and each webmaster can manage the backoffice in the native language (german or french).
Oops! The plugin worked for a while on WP 3.8 although it's not declared as 3.8 ready.
I finally got an error message:
Fatal error: Call to undefined function is_user_logged_in() in /wp-content/plugins/user-language-switch/user-language-switch.php on line 117.
Could you update please?