To add a bit more to my question, I'm wondering if the words are used interchangeably, or if 法度 has more a sense of law that is set up to ban or prohibit something? Is 法度 a commonly used word?
法律 is the general word for "law", as in 「法律を守る」(obey the law),「法律で禁止されている」(forbidden by law) or 「渡辺法律事務所」(Watanabe Law Firm).
I believe that the most common use of 法度【はっと】 is to mean "something that is terribly bad manners", and that it's almost always used with ご in front — 「ご法度」. A quick Web search found:
"Talking about the bride and groom's ex-lovers is a no-no: faux pas that guests mustn't make at weddings"
It seems that originally, 法度 meant a law forbidding something, but I don't think it's used in modern-day legal discussions.
First, 法律 is more commonly used in spoken and written Japanese than 法度 is. You can verify this notion by how the two words appear in a Google search, with 404 million for the first and 930,000 for the second. Also, ほうりつ when entered in an input bridge will immediately convert to 法律, whereas はっと will likely convert to Katakana, and only with further keyboard work will you get 法度.
That said, the two words have similar meanings. Using Kenkyusha's as my source here,
法律 applies to "(the) law" as well as referring to a law or legislation. It is likely the most general word for this idea, and does not have the specific sense you note for 法度 in your question.
法度 also means a law or ordinance, but also can refer to a prohibition, ban, or taboo.
On a personal note, in over 20 years of translating Japanese material into English I've never seen 法度 whereas I regularly see 法律. However, I am not a legal translator or scholar, and input from someone with that background could further clarify this question.