How to use a custom post type archive as front page?

After you have set a static page as your home page you can add this to your functions.php and you are good to go. This will call the archive-POSTTYPE.php template correctly as well.

add_action("pre_get_posts", "custom_front_page");
function custom_front_page($wp_query){
    //Ensure this filter isn't applied to the admin area
    if(is_admin()) {
        return;
    }

    if($wp_query->get('page_id') == get_option('page_on_front')):

        $wp_query->set('post_type', 'CUSTOM POST TYPE NAME HERE');
        $wp_query->set('page_id', ''); //Empty

        //Set properties that describe the page to reflect that
        //we aren't really displaying a static page
        $wp_query->is_page = 0;
        $wp_query->is_singular = 0;
        $wp_query->is_post_type_archive = 1;
        $wp_query->is_archive = 1;

    endif;

}