It might be a reference to the fact that the Celtic temperament is traditionally seen as sensitive, romantic, visionary, poetic ... but on the other hand it might not.
We need you to give us some more information about the context: what's the title of the film and where's it set? What sort of person is the father and is his daughter similar to him? And so on....
Later edit: Ah, it's just struck me - this is from the film Saving Mr Banks, isn't it? Said by the father of the little girl who later became P L Travers, the author of Mary Poppins?
Then, although this part of the film takes place in Australia, P L Travers' father was Irish by descent. He's romanticising his [irresponsible] approach to life by saying that it's due to his Irish temperament; and he's telling his daughter that she has the same temperament. "We share a Celtic soul" is a 'poetic' way of putting it.