It is not permissible for a man who believes in Allaah and the Last Day to touch a woman who is not his mahram. For details of evidence and views of the scholars, please see the answer to question no. 21183
With regard to whether wudoo’ is broken by touching a woman, there is a difference of opinion among the scholars. The correct view is that it does not invalidate wudoo’ – see question no. 2178 – and it makes no difference whether the woman is his mahram, his wife or a non-mahram.
And Allaah knows best.