After I posted I’ve added two lines to the code, now it works fine!
if (WPGlobus.language == 'nl') {
jQuery('.wpglobus-current-language a span').html("EN");
jQuery('.wpglobus-current-language a span').removeClass('wpglobus_flag_nl').addClass('wpglobus_flag_en');
jQuery('.wpglobus-current-language a').attr('href', location.origin + '/en');
} else {
jQuery('.wpglobus-current-language a span').html("NL");
jQuery('.wpglobus-current-language a span').removeClass('wpglobus_flag_en').addClass('wpglobus_flag_nl');
jQuery('.wpglobus-current-language a').attr('href', location.origin);
}