As per the Act of Union 1800, which restates the provisions of the Act of Settlement 1701 and the Bill of Rights 1689, those who have ever been Roman Catholics are disbarred from succeeding to the British Crown. Likewise, a person who marries a Roman Catholic is disbarred.
Apparently not, lafrancaise. He was Catholic and their children were brought up as Catholics, but she seems to have remained a Protestant. This link illustrates the muddle that we are in (apart from atheists like me of course).
I remember years before Prince Charles married Diana, he was linked with Princess Marie-Astrid of Sweden, but people were saying that although she was 'suitable' in all other ways, he would have been unlikely to marry her because she was Catholic.