A DateTime value has no format. Internally it's just a count of ticks since the epoch, 0001-01-01 00:00 in .NET. Formatting is when you call ToString.
Just use a different CultureInfo for the culture that has the calendar you want, e.g.
CultureInfo french = CultureInfo.GetCultureInfo("fr-FR");
String nowStr = DateTime.Now.ToString( french );
Use CultreInfo.InvariantCulture if you just to use a predictable Western culture with a Gregorian calendar.