Custom Post Type setup

You can set any arbitrary path in the rewrite slug and has_archive arguments:

$args = array(
    'rewrite'     => array('slug' => 'people/researchers'),
    'has_archive' => 'people/researchers',
    // other args...
);

EDIT

Your post type slug is researchers, so WordPress will be looking for the file archive-researchers.php by default. If you want to force a different template, you can use the archive_template filter:

function wpd_researchers_archive_template( $archive_template ){
     if( is_post_type_archive( 'researchers' ) ){
          $archive_template = locate_template( 'archive-people.php' );
     }
     return $archive_template;
}
add_filter( 'archive_template', 'wpd_researchers_archive_template' );