Ok, found the solution on my own. Was just tweaking the css.
Here my solution if it helps someone else:

/** WPML language switch to the right **/
.sub_menu {
float: right;
}

/** WPML no flags but DE, FR **/
.language_flag img {
display: none !important;
}

.language_code {
display: block !important;
text-transform: uppercase;
}

/** WPML alignment language switch text**/
.avia_wpml_language_switch {
top: 0px;    /** correct alignment **/
padding-left: 30px;
}

#top ul.avia_wpml_language_switch li {
margin-left: 10px !important;  /** gap to phone div **/
}