Finn is the love interest of Rose Tico in the the Star Wars sequel trilogy.
He is the best friend of Poe Dameron, with whom he also has a relationship that can be interpreted as having romantic tension. He is also Rey's best friend, whom some fans speculate that he might have a small crush on. Finally, in The Rise of Skywalker, he might be the love interest of Jannah.
In The Last Jedi, Rose stops Finn from running from the Resistance again. Then, he and Rose go on a mission together to the Canto Bight cassino to find the codebreaker and they start to grow closer. Rose tells Finn about her sister and her perspective on the war which influences his reflection about his place in the war. During their adventure, Rose shows signs of having developed feelings for Finn, which are more explict in the novel version. It's because of Rose that Finn decides to stop running from the Resistence and finally defines himself as part of the "rebel scum" to Captain Phasma.
At the Battle of Crait, when Finn decides to sacrifice himself by flying his speeder into the First Order's battering ram cannon, Rose crashes her speeder into his, stopping him. When he asks her the reason why she did it, Rose replies that the way to win is "not fighting what we hate, saving what we love", which is her way to confess her feelings for him. Then, she kisses him on the lips and falls unconscious from of her wounds. Finn carries her out of the battlefield and, at the end of the movie, Finn is seen with a still unconscious Rose in the Falcon placing a blanket on her, showing that he cares about her.
In The Rise of Skywalker, Finn invites her to accompany the group in the mission to search for the holocron, but she is assigned other tasks by General Organa, so she declines. Later, when Finn and Jannah stay behind to disable the transmitter of the Steadfast during the battle of Exagol, Rose doesn't want to leave Finn behind. She only leaves after being persuated by other resistence members.
Possible Love Interests
Poe is Finn's best and first friend. In the sequel trilogy movies, they had a lot of chemistry together and many fans interpret several of their scenes as having romantic and sexual undertones.
In The Force Awakens Finn helps Poe to escape the First Order as the first act of defection in the beginning of the movie. Then, Poe is the one that names him "Finn" after not liking the name the First Order had gave him. When their ship crashes in the Jakku desert, Finn keeps his jacket thinking Poe died from the crash. Later, when the First Order attacks Maz's castle on Takodana, Poe and the Resistance arrive to help defend the castle and Finn watches Poe's ship and screams "That's an hell of an pilot" without knowing that it is in fact Poe on it. They finally reunite again after the battle, and run to embrace as soon as they see each other. They are both happy to see each other alive after the crash and when Finn tries to hand back Poe's jacket, Poe tells him that he can keep it because it suits him.
In The Last Jedi, Poe is the first one that Finn sees after waking up from the injury he received from Kylo Ren in the end of the previous movie. Poe stays by his side and seems concerned with him.
In The Rise of Skywalker, Finn, Poe, Chewie and Rey go to search for the holocron together. When Finn tries to say something to Rey but is interrupted, Poe gets very curious. He keeps asking Finn what was he was going to say to Rey several times in the movie. Some viewers interpret this as Poe being jealous. Later, they both support each other while attacking stormtroopers on the corridor of the First Orders ship they infiltrated to rescue Chewie. Then, when Poe gets shoot in the crossfire, Finn immediately stops to go see if he is fine, which leads to them both being captured. When they are about to be executed by Hux and the stormtroppers, Poe chooses this moment to ask again what Finn wanted to tell Rey, which is plays as a joke in this tense scene, but Poe seems very hurt that Finn is hiding something from him. Afterwards, in the end of the movie, the two of them reunite after the final battle and they embrace each other again, before Rey arrives and joins them.
Poe's actor always hinted a romantic tension between his character and Finn. In an interview for the The Rise of Skywalker, he states that he always found their relationship interesting and that he played with the intention of being romantic, but that Disney was still not ready to show this kind of representation on screen.
Finn is also best friends with Rey. In The Force Awakens, he did have a chemistry with her and many fans thought she would be his love interest. During the sequel trilogy movies, mostly in the first one, there are some ambiguous moments that can be interpreted as him either having a small crush on her or just being a very good and close friend to her.
In the The Force Awakens. When they were running from stormtroopers, he kept grabbing her hand. When asking why she wants to go back to Jakku, he asks if she has a boyfriend. When Finn is about to leave with Sido Ithano's crew, he asks Rey to come with him and tells her to take care of herself. When Rey is captured by Kylo Ren, Finn goes to Starkiller Base not to disable the shields but to rescue her. Rey also shows affection towards him when she kisses an unconscious Finn on the forehead, before goes to find Luke Skywalker at the end of the movie.
In the end of The Last Jedi movie, when the two friends finally reunite they embrace each other.
In The Rise of Skywalker, Finn tries tell her something but is interrupted. Some fans believe that he wanted to confess his feelings for her, but the movie never reveals what he was trying to say so it is very open to the viewers interpretation. According to the cast of the movie, including Finn's actor and the movie director, he wanted to tell her that he was force sensitive.
In The Rise of Skywalker, Finn meets Jannah and is suprised to know that she was also a stormtrooper that defected from the First Order, because before meeting her he was unaware that there were others like him. The two of them become close fast because of their shared past and this causes them to lead the assault during the battle of Exagol in the end of the movie. Some fans believe that the movie implies that she is a new love interest to him.