Many zoo animals form long-term, deep-seated bonds that zookeepers often describe in terms of companionship and "romance": Point Defiance Zoo , these two are described as longtime companions.
Knowing if this is a movie, a specific blog post, or a series you found online would help in identifying the "relationships and romantic storylines" you're looking for.
Some zoo animals form long-term monogamous relationships, mirroring those of humans. For example: