No story exemplifies this better than The Strange Case of Dr. Jekyll and Mr. Hyde . While not a literal animal, Hyde is described in simian, bestial terms, representing the regression to a primitive state. The "romantic" element here is the seduction of the wild. The civilized man is drawn to the freedom of the beast.
A rarer but more poignant form involves a fully non-human animal (intelligent but non-shapeshifting) in a romantic-coded relationship. Films like The Shape of Water (the amphibian man) or the novel The Last Unicorn (the unicorn and the prince) navigate this space. Here, the animal cannot become human. Love becomes an act of translation. Animal And Man Sex.com