One more idea, inspired by Josh's answer, using a Queue instead of shifting the array.
var days = CultureInfo.CurrentCulture.DateTimeFormat.DayNames;
if (CultureInfo.CurrentCulture.TwoLetterISOLanguageName == "en")
{
var q = new Queue(days);
q.Enqueue(q.Dequeue());
days = q.ToArray();
}