Catherine Zeta Jones has a Welsh father (Dai Jones) and a mother (Pat Fair) who is of mixed Welsh and Irish ancestry. CZJ was raised Catholic reflecting her Irish ancestry. Her middle name is from her grandmother whose father served on a ship called "Zeta".
There seem to be a lot of mis-information on the internet about her ethnicity, some perhaps intentional. She is erroneously said to be of Greek ancestry due to a mistake on a CNN transcript of the Larry King show.
I believe it is a Coton De Tulear. That's my opinion!!