Q: What language would Adam and Eve have used or spoken?
A: The original language of mankind was Hebrew. Adam and Woman spoke Hebrew, as did their descendants until the Tower of Babel in Genesis 11. We know this to be true because of the etymology of the names of people recorded in chapters 1-10. In these chapters prior to the Tower of Babel, all names have meaning only in Hebrew.
For example, the name Adam is the Hebrew word for "earth", while the name Eve in Hebrew means "life". These names have meaning in no other language besides Hebrew, which would indicate the original language was Hebrew. After the Tower of Babel, God created many new languages to scatter mankind. From Chapter 11 onward, the names of biblical characters may have meaning in other languages.