There is a story in the Bible that Adam and Eve ate the fruit and sinned against us god. But other religions, including some Christians, describe that they were having intercourse and that's why God threw them out of the garden. Which Christian groups believe this, and what is their reasoning?
I believe that you are referring to the theory that the original sin was sex. This, however, is not Biblically true. Before the fall, God said:
How could they multiply if sex was a sin? The original sin, according to the Bible, was disobedience. (See Genesis 3)
EDIT: Because the question was edited, my answer has now been edited too. I have ran into a few people, mostly from the Catholic faith, who believed in this teaching. As far as I know, this is not Catholic doctrine, they just had been misinformed.