There may not be a lot of fanfictions with this very specific scenario. However, some Naruto fanfictions that deal with Naruto in unexpected situations might be a start. You could also join Naruto fanfiction communities or forums and ask fellow fans if they know of any such stories. They might be able to point you in the right direction.
I'm not sure of a specific fanfiction with this exact plot. But you could try searching on popular fanfiction platforms like Fanfiction.net or Archive of Our Own. Look for Naruto fanfiction categories and use the keywords 'pregnant Naruto runs away' in the search bar.
One possible fanfiction could be where they run away to avoid a false accusation in the village. They might head to a far - off land, discover new powers, and form a stronger bond. In this story, they face many challenges together, like dealing with strange creatures and harsh terrains.
There are fanfictions that involve Sakura being pregnant in an alternate storyline. It might show how the village reacts to the news and how her friends, like Naruto, step up to help her. It could also delve into the medical aspects of her pregnancy, considering Sakura's skills as a medic - ninja.
Perhaps she feels alone. If the father of the baby is not around or is not supportive, she might feel like she has no one to turn to in the village. So, she decides to run away to start anew somewhere else where she can raise the baby on her own terms. Also, she could be running away from her own responsibilities as a ninja. The pregnancy might make her question her role and future in the ninja world, and she chooses to escape from it all.
One consequence could be that his friends worry about him a great deal. They might go on a search for him, which could put them in danger as well. After all, they care about Naruto deeply and won't just let him disappear without trying to find him.
One possible story could be that Legolas runs away from his duties in Mirkwood because he feels suffocated by the strict rules. He goes on a journey to discover himself, meets new friends along the way, and learns different cultures. This newfound freedom allows him to grow as a character and become more in tune with nature in a different way than he was in his homeland.
One great 'pregnant Naruto fanfiction' is 'Naruto's New Family'. It focuses on Naruto's journey as he discovers his partner is pregnant and how he prepares for fatherhood in the ninja world. It has really interesting character development and shows Naruto in a different, more mature light.
She could also be running away to protect the baby. There might be some sort of danger or negative influence in her current place. For example, if there are people who would harm the baby or if the society she lives in is very judgmental towards unwed mothers.
It could be that Naruto and Temari run away because of a misunderstanding. The village leaders think they are traitors. But in reality, they are on a secret mission to stop an evil force that is about to attack both of their villages. They run away to gather allies and resources in secret, and during their journey, they face many difficulties that test their friendship and determination.
One possible plotline could be that Naruto and Gaara run away to avoid a false accusation in their villages. They might journey together, facing various challenges like harsh terrains and lack of supplies. Along the way, they could bond over their shared experiences of being outcasts in the past. Naruto might use his optimism to keep Gaara's spirits up, and Gaara could use his sand powers to protect them from potential threats.
It could also be that they run away to pursue a personal goal. Naruto has always wanted to find a way to truly bring peace to the ninja world and Sakura believes in his vision. So they run away from the village to seek out a powerful jutsu or a long - lost artifact that could change the fate of the ninja world for the better.