Lost in Austen
I'm probably the last one to find out about this, but I just watched Lost in Austen, a British television show from 2008. It was really fun! I can't believe I'd never heard of it.
Amanda Price, a 21st century woman, changes places with Elizabeth Bennet from Pride and Prejudice, who inexplicably shows up in her bathroom.

Among the amusing things that happen is that Elizabeth fits right in, whereas Amanda has a terrible time, despite knowing everything that is going to happen. Here they are in the same room near the end where Elizabeth is quite settled, but Amanda is still struggling ("Elizabeth Bennet is lending me her mobile.").

I shouldn't say Amanda knows everything that is going to happen because a lot of the fun comes from alternative events that do not happen in the novel. Not every character is what they seem.
I watched it on SHOUT!TV , which has the American version apparently. It is missing this scene where Amanda sings Downtown. I'm not sure why. Some legal reason maybe? It doesn't really matter because we can infer it from what happens after. Indeed I thought it was kind of clever what they had done, not knowing the scene had merely been cut.
In any case, I really enjoyed watching it and I consider it a failure of the entire internet that this has existed for over 15 years without my knowledge.