Well, he might be really surprised. Some fanfictions could show Boruto in situations he never imagined. He could be proud of the creative ideas fans have about his son's adventures.
If Naruto watches Boruto fanfiction, he may have mixed feelings. He could find some of the stories really heartwarming, especially those that show strong family bonds. However, he might also be a bit shocked at some of the more out - there plotlines that don't quite fit with his view of the ninja world. For example, if there are fanfictions where Boruto has some super - strange powers that go against the normal chakra system, Naruto would be like 'What's this?' But overall, it would be an interesting experience for him to see how fans perceive his son and the new generation of ninjas.
He would probably be quite intrigued. Naruto has always been about believing in the next generation. When he reads Boruto fanfiction, he may see different versions of Boruto's growth and development. He might get inspired by some of the ways fans depict Boruto facing challenges. And he would surely enjoy the parts where Boruto is shown to be a great ninja, just like he always hoped his son would be.