Get custom post type slug for an archive page

To get the current post type use get_post_type(). Then ask get_post_type_object() for all the data you need, for example the slug:

$post_type = get_post_type();
if ( $post_type )
{
    $post_type_data = get_post_type_object( $post_type );
    $post_type_slug = $post_type_data->rewrite['slug'];
    echo $post_type_slug;
}