Romance is basically nonexistent, there are several that like him but he does not really notice it. Not so much out of being dense but more that he still very much has lost a lot of his ability to feel emotions. The novel goes more in depth on his thoughts but for the most part he just is desensitized, its why he can joke like a moron in the middle of a battle where people are literally killed seconds prior. Gaston towards the end of the novels said that he like the other immortals you meet later are all varying degrees of insane and that he hopes he will be able to open his heart to humans again at some point. There is however a comedic chapter in the epilogue where all the girls
who are in love with him have a contest to monopolize him for the day. He was tricked into becoming the prize, It was hilarious.