Not really. Naruto has always been interested in the stories of the ninja world. Fanfiction is just another form of those stories, just more fan - created. So it's not that strange for him to be curious about what fans think about his son's story.
The popularity of 'Boruto watching Naruto fanfiction' comes from the fact that it taps into the nostalgia of the Naruto series while also bringing in the new elements of Boruto. Fans of the original Naruto series are curious to see how Boruto would perceive Naruto's journey. It also gives fanfiction writers a chance to be creative, imagining different ways Boruto could be involved in Naruto's past, like if he was able to give Naruto advice during a difficult battle or if he could prevent certain tragedies from happening in Naruto's life. This type of fanfiction can be both heartwarming and exciting, which is why so many people are drawn to it.
One great 'Boruto watching Naruto fanfiction' could be where Boruto discovers an old journal of Naruto's adventures and reads it, getting a whole new perspective on his father. It's really interesting as it shows Boruto's growth in understanding Naruto.
In most cases, it is legal. Fanfiction is often considered a form of derivative work. As long as it doesn't violate any copyright laws in terms of excessive use of copyrighted material without permission in a way that goes against fair use, it's okay. For example, if a fanfiction writer is just using the Boruto characters in new and creative scenarios, it's generally fine.
Naruto might feel a bit of nostalgia. He would see elements of his own past and how the new generation, like Boruto, is being portrayed in these fictional stories. He could also be proud to see how much his son has inspired fans to write so many different stories.
Naruto would likely be excited. He loves his son so much that seeing different stories about Boruto would be like seeing different potential futures for him. He might even get some inspiration from the fanfiction to give Boruto some advice in real life.
One possible plot could be Naruto seeing a future where his friends are in danger. So, he starts training harder in the present to prevent that future from happening. He might see a powerful enemy that his friends can't defeat alone, and this knowledge gives him the motivation to gain new powers or improve his existing skills.
He would likely be very curious. Naruto has always been eager to learn and explore new things, so seeing future fanfiction would be like opening a door to a new world of possibilities for him.