He probably gets very worried. Kakashi is Naruto's teacher and mentor, so he'd likely be immediately concerned and rush to Naruto's side to assess the situation.
Kakashi would likely be very concerned. He would immediately assess Naruto's injuries. If they were serious, he would use his medical skills to start treating him right away. His first reaction would be to make sure Naruto was stable and out of immediate danger.
Kakashi might immediately offer a comforting presence. He could put his hand on Naruto's shoulder and just be there silently, letting Naruto know he's not alone.
Well, Kakashi is a complex character. When he discovers Naruto is abused in the fanfiction, he may first feel a deep sense of guilt for not noticing earlier. He'd then use his skills and influence in the village. He could start by reporting it to the proper authorities in Konoha, like the Hokage. And at the same time, he'd be there for Naruto, providing emotional support, talking to him, and helping him through the trauma. Kakashi has his own past traumas, so he'd understand what Naruto is going through on some level.
He'd probably be a mix of angry and sad. Angry at whoever or whatever caused Naruto to be in this state, and sad because he cares about Naruto so much. He might clench his fists tightly, trying to control his emotions while he focuses on helping Naruto. He'd also feel a sense of guilt, wondering if he could have prevented this from happening.
One possible plot could be that Naruto was on a mission alone and got ambushed by a group of rogue ninjas. Kakashi, while out on his own patrol, stumbles upon the injured Naruto. He quickly takes Naruto to a safe place and uses his medical ninjutsu to stabilize him. Then, he might start to investigate who attacked Naruto and why, leading to a revenge - based sub - plot or uncovering a larger conspiracy against Konoha.
You can try fanfiction websites like FanFiction.net or Archive of Our Own. Just search for 'Kakashi finds baby Naruto' on their search bars, and you'll likely find some relevant fanfictions.
One possibility is that Kakashi would immediately use his medical ninjutsu to treat Naruto's wounds if he has the skills. Then he'd try to calm Naruto down by talking softly to him, asking what happened. He might vow to protect Naruto better in the future and start investigating the cause of Naruto's harm.
One possible reason could be that Naruto is feeling lonely. Despite having friends, there are times when his past as an orphan and the years of being shunned by the villagers resurfaces, making him feel isolated. Kakashi finding him in such a state might then lead to a heart - to - heart conversation about Naruto's inner struggles.