in my function.php i have :
// WPML
 function set_icl_adjust_id_url_filter_off($off){
        global $icl_adjust_id_url_filter_off;
		$icl_adjust_id_url_filter_off = true;

}
add_action('init','set_icl_adjust_id_url_filter_off');


and i then i do this :
$lang=ICL_LANGUAGE_CODE;
if ($lang=="fr") {
	 $idFR=$inst->term_id;
 // GET THE ORIGINAL ENGLISH ID OF THE INSTRUMENT with the French ID
    	$idEN= icl_object_id($idFR,'pa_instruments',true,'en');
 // GET THE ORIGINAL SLUG WITH THE ENGLISH ID
	 $slugFR= get_term_by('id',$idFR, 'pa_instruments');
	$slugEN= get_term_by('id',$idEN, 'pa_instruments');
	echo "<div style='position:absolute;top:".(20*$nn).";left:0;z-index: 999;background:#FFF'> slugEN: ".$slugEN->slug. " <br>slugFR: ".$slugFR->slug." </div>";
	 $theSlug=$slugEN->slug;
	   }


I also tried like sarah proposed with

global $sitepress;
remove_filter('get_term', array($sitepress,'get_term_adjust_id'));
$slugEN= get_term_by('id',$idEN, 'pa_instruments');
add_filter('get_term', array($sitepress,'get_term_adjust_id'));

but it didn't work...

thanks