I found the solution. I had to flush rules after I change the search base with the code on the edited question. Here is the final code:
$lang = get_bloginfo("language");
if ( $lang == 'de-DE' ) {
add_action('init', 'search_base_german');
function search_base_german() {
$search_slug = 'suche'; // change slug name
$GLOBALS['wp_rewrite']->search_base = $search_slug;
$GLOBALS['wp_rewrite']->flush_rules();
}
}