I’m a big fan of time travel stories but they’re at their best when the person going back in time is just... some random person. No scientists, no historians, no super soldiers. That’s why Back to the Future is one of the best. Marty is just... a dude. Not even a particularly intelligent dude. Just some dude that knows a scientist.
In the future, the Professor invents a time portal. He has a lab assistant he has a close relationship to, but the student is there more for pay than his great scientific knowledge or aspirations. The Prof wants to send the student on the first test trip and the guy asks why him and not the Prof. The Prof says he needs to stay behind to monitor and the student can't operate the machinery. The Prof wants to see what kind of effects a non-scientific mind would have on the past and how dangerous it could be. The guy jokes that the Prof could have just said that he is stupid and expendable.
Prof has prepared a time where our lead should be free from any lasting effects on the time space continuum. The guy is given a jacket and pants from their time designed to resist the elements and some super nutrition bars in case of emergency. Otherwise, he’s just bringing small supplies, a change of period appropriate clothes, and a little money. The trip will be roughly a year, limited due to the position and alignment of the planet and time. While the Prof can pull him out of the past in an emergency, it will be a violent pull, will probably have some health effects, and would ruin the experiment, so they want to avoid that.
Our protagonist goes back to a middle ages-esq time. The trip makes him violently ill and his future understanding of the language is too proper to meaningfully converse with the locals, and he passes out outside of town due to the time jump. He wakes up to a young woman poking him with a stick. She accuses him of being a soldier/spy because of his outfit and the change of clothes she found, but eventually our lead convinces her he's a scientist/teacher and she agrees to not kill him.
She lives outside of town after her parents died and over time the villagers shunned her for witchcraft or superstitions based on her family dying. She teaches him to fix his language skills, and they befriend each other (not played for romance). He helps her with chores and such but he accidentally mentions some modern things from time to time and she pushes him to tell her things (believing him to be a scientist and the things he speaks of are just advanced tech they have in the larger cities or other countries, no mention of time travel).
He tries to teach her as much as he can (gravity, heliocentric universe, penicillin) but since he's just an average guy, he can't prove bacteria or make a battery or anything super useful. Trying to explain anything he’s actually skilled in from working in the Prof’s lab is so advanced to her and he can’t explain the basics of creating a computer and the Internet and such that he just looks like an idiot trying to convince her. He teaches her the few things he can, like how to read, about space, and some bits about taking care of yourself when sick and they become great friends.
As seasons change, he has to tell her that he'll be leaving sometime (not sure when without a good calendar so all he has is moons to go on). She reacts poorly, mostly out of sadness and anger, and accuses him of mocking her with his stories and fake science; that she was just a game before he leaves to some other town. He does a poor job of saying how much he respects her and that he knows things because he was taught them, but she has had her entire world view challenged and she's actually learning, so he thinks she's smarter than he is. In her anger, she takes that to mean he sees her as an experiment and kicks him out.