In this case it is very simple because the month starts on a Tuesday. Regardless of how you interpret "third week" you almost certainly arrive at the same week.

It's much more confusing when the month starts on a Saturday. In that case you might say the first week begins on the second day of the month, so the first day of the month is the zeroth week. Or the first day of the month could be the first week and second day could be the beginning of the second week. It depends on how you interpret it.

I found this interesting discussion on the subject: Denotation of the "n-th Week of the Month/Year"

Also note that "European" is rather vague. Do you mean Greek Orthodox or some other type of European?