Display CPT index page as front/home page

Rename portfolio-archive.php to front-page.php and change the post type for that page with a filter on pre_get_posts:

add_filter( 'pre_get_posts', 'wpse_99860_portfolio_on_front' );

function wpse_99860_portfolio_on_front( $query )
{
    // not the main loop
    if ( ! $query->is_main_query() )
        return $query;

    // not the front page
    if ( ! $query->is_front_page() )
        return $query;

    $query->set( 'post_type', array ( 'portfolio' ) );

    return $query;
}