"Rappaccini's Daughter" is definitely a love story of sorts, so I believe that a strong case can be made that Giovanni is in love with Beatrice. It is not hard to imagine why he would fall for such a girl, either. She is from a financially fairly well-off family, she is an especially beautiful woman, and there is an air of mystery about Beatrice that increases his attraction to her. Readers are given evidence that supports the idea that their connection is deep and real and not only a physical, surface-level attraction. Readers get lines of text that indicate that a spiritual connection exists between Giovanni and Beatrice:
she was now the beautiful and unsophisticated girl whom he felt that his spirit knew with a certainty beyond all other knowledge.
On the other hand, I do think an argument could be made that Giovanni isn't actually in love with Beatrice. He is definitely attracted to her. That I don't think can be argued against. He is initially attracted to her beauty and mystery, and I think that Beatrice's mystery might have become the main attraction. She is like a puzzle to him, and he wants to know the answer. It's why he buys her flowers in order to see if they will or will not wilt in her hands. He's giving her a test, and that doesn't exactly connote love. By the end of the story, Giovanni likely knows that the changes happening to him allow him to be with Beatrice, yet he pushes the "antidote" on her. He wants her to change into something other than the girl he knows, and that again doesn't resemble love in my opinion.