Noah seems to make decisions based on T not F. Remember when he asks Allie, "what do you want?" That seems logical, not feeling focused, to me. Why decide which man to be with based on what other people want and how it will affect them and fears of hurting people (F)? Why not decide based on what you want, the simple and logical way to decide? It's logical to make a decision based on what one wants to happen. It is more feeling centered to make a decision based on who will be affected.
And there are other examples, but this is the one that initially comes to mind since I haven't read or seen the movie in a while. He just seems to think and decide in a slightly more logical way than a way based on feeling. I think it's hard to see that due to his love for Allie trumping logic. However, desperate attempts to preserve love (like trying to make Allie remember despite her illness that logically prevents her from remembering) are human, not personality.
I mostly think Noah is an ISFJ for a few reasons, his most defining qualities revolve around big expressions of values, judgements and feelings. He enlists in the war because he wants to help his nation and wants to fight along side his fellow Americans and country he loves. Fe is concentrated on making bringing things together and pushing values outward to create something within a community. His enlisting seems very Fe-ish. Secondly he writes Allie nearly 400 letters that's a lot of dedication and time to give to a single person. Again this is outward feeling, most introverted feeling types don't readily revel what is most precious to them, but Noah put's his heart and soul into those letter. Lastly Noah builds Allie her dream house with everything she ever wanted. He basically dedicated a love monument to her. If that isn't an example of Extraverted Feeling I don't know what is. He basically built a house to show her he loved her and didn't forget about her even though she had moved on with Lon.
Building a house for your ex-girlfriend is not logical nor logic based. He is ruled by feelings over thinking. That's not to say he can't be logical at all. Fe-Ti are linked, but it's obvious he has a feeling preference and his feelings take priority and preference over his thinking. All of his actions are very Fe, his judgments effect the outward world and aim to change, alter or shift it in some way, that's an FJ aspect.
Sometimes in extreme situations people can be overruled by their inferior functions. At first I thought Noah was INFP because Te could cause him to be "You know what, WHAT DO YOU WANT?" And I'm not sure if it makes complete sense anymore because Noah has a lot of Fe, and INFPs have Fi. So I'm thinking Noah is probably primary Fe. Everything he does is for other people.
So xxFJ as well because those are the most obvious parts of his personality. He is also branded by his dependability, which I think is more an xSFJ thing. And Noah is obviously an introvert. . . so ISFJ. He kinda threw things in Ally's face at the wrong time, things that had happened in the past. Si-Fe-Ti-Ne makes sense for Noah because of his infamous "What do you want?" comment. Ti just wants the truth in the end. It's kinda pairing with Fe to make it an emotional consideration. I think he used his Ne to make Ally's dream house, because he had to assemble all the details he had with Si into a singular project. But in the end he just wanted the best for Ally, even after he had gotten aggravated with her so many times.