Good morning, Tesia! How interesting that you are tone deaf but speak 3 languages. Did your learn your second and third languages as a child or later in life? Were you in an immersion situation when you learned them, such as residing in a country where the language is spoken?
In spite of my tone deafness and difficulties speaking another language, I too am good with accents. When I was trying to speak Spanish, my accent was acceptable for an English-speaker, but my pronunciation of words was not.
I am not a linguist, a neurologist or an audiologist so I can’t explain the difference between how we hear and process accents and the pronunciation of words, but they do appear to use different faculties. My husband, who immigrated to the United States when he was almost 30, speaks fluent English but with a very heavy Argentinian accent. He hasn’t been able to master the American accent at all. Yet, he is also fluent in Italian and Brazilian Portuguese and masters those accents to the point people believe he is a native. No one would ever believe he is a native American!! The type of accent may matter also.
I have done some light online research about tone deafness and speaking foreign languages and found articles that mentioned a correlation and others that debunked the idea, but most of what I read was written for and by people who are linguists or neurologists and way too technical for my complete understanding.
Some articles confirmed a relationship for learning tonal languages like Chinese but I didn’t find much for foreign languages in general. However, there was a lot written about different levels and types of tone deafness. One suggested different methods of teaching music to those who are tone deaf. I assume different approaches to teaching languages may also help.
Again, my piece was definitely not a scientific study! However, my experience and the experiences of others lead me to believe there is a correlation of some sort and degree between tone deafness and language learning.