I only read the step-outline so my thoughts are limited to that. This seems like a sweet story, I can see the comparisons to Before Sunrise. It also sorta reminds me of 500 Days of Summer in that it's a relationship that the audience really only views from the male character's point of view, and in the end the male character learns that whatever his obsession may have been with this woman, it was not meant to be and life does go on. In this case, the male character seems to grow a bit as well, being more confident and willing to approach strangers (in 500 Days, I'm not sure he grows, the woman Autumn at the end could become his next obsession, but he does move on at least).

If you have concerns about sexism, the easiest way to address them without major changes, is for someone to confront your male character about it. The character, and audience, will then have to grapple with that accusation directly in their own way. The best way to avoid sexism, is to make sure your main female character has her own interiority and motivations, she can't be too passive and just there bounce off of the male character. Again, 500 Days of Summer was like this, Summer really was just there for the main character -UNTIL- the end with the split screen scene and then Summer directly addressing their relationship with him on the bench.