WP Custom post type on frontpage vs WPML

<?php
// -------------------------
// In my functions.php file...
// -------------------------
add_filter( 'pre_get_posts', 'my_get_posts' );
function my_get_posts( $query ) {

    if ( is_home() && $query->is_main_query() )
        $query->set( 'post_type', array( 'post','objet', 'etude_de_cas' ) );
        $query->set('orderby','post_type date'); // sort by type, then by date.
        $query->set( 'order', 'DESC' );

    return $query;
}

// -------------------------
// in my front-page.php file...
// -------------------------

while (have_posts()) : the_post();

$count++;

$class = ($count ===1) ? 'first ' : '';

$post_type= strtolower(get_post_type( get_the_ID()));

if($current_type != $post_type){

    switch ($post_type){
    case 'post':
        // Tête de gondole
        $section_title= _('Agencements');
        $section_link= '<a href="#" class="button-black">'._('Voir tous les agencements').' &#8250;</a>';
        $thumb_size= 'gondole';
        $ul = '<ul class="wrap">';
        $class .="teaser";
        break;

    case 'etude_de_cas':
        $section_title= _('étude de cas');
        $section_link= '<a href="#" class="button-black">'._('Voir toutes les études de cas').' &#8250;</a>';
        $thumb_size= 'gondole';
        $ul = '<ul class="wrap">';
        $class .="teaser";
        // Etude de cas
        break;

    case 'objet':
        $section_title= _('Le stock');
        $section_descr = _('Derniers objets');
        $section_link= '';
        $thumb_size= 'vignette';
        $ul = '<ul id="og-grid" class="og-grid product-listing">';
        $class .="latest";

    default:
        // Stock
        break;
    }
    $current_type = $post_type;
    if($count>1){ ?>
</ul>
<hr>
</section>
<?php
    }

    echo "\n".'<section class="row '.$class.'"><h1>'.$section_title.'</h1>';
    echo (strlen($section_link)>0) ? '<p class="text-center">'.$section_link.'</p>' :'' ;
    if($post_type ==='objet'){
        echo bones_wpsearch();
    }
    echo ($section_descr!='') ? "\n<h3 class=\"aligncenter\" style=\"text-transform:uppercase\">".$section_descr.'</h3>': '';
    echo $ul;
}
// Now render the items
if($post_type==='objet'){
    get_template_part( 'content', 'objet' );

}