So many problems here.
I’m a little fuzzy on this exact moment in history, but we’re not talking about an enlightened era in British history. Henry I may have felt his daughter was fit to rule, but he didn’t feel he could put her on the throne unmarried.
When Christ and His Saints Slept by Sharon Kay Penman is a really good look at the events following Henry’s death in 1135. So, this is probably something you should read regardless.
Women, even noble women were being explicitly denied access to education, and there’s a legitimate question of if your character would even be literate. (Expect language to come up again in a second…)
For her family, she’d be too valuable as a potential political bargaining chip to simply send off into combat. They could marry her off in exchange for concessions from another house, or to cement an alliance.
As a member of a minor noble house she couldn’t even rely on her opponents capturing and ransoming her on the battlefield. She’d be just another random combatant they didn’t recognize and snuff her.
Now, if she’d run away from home, disguised her gender and joined a mercenary band, this would make sense. And it wouldn’t actually be anachronistic.
Seriously, if you’re wanting to run with this character, running away, disguising herself as a man and signing on with mercenaries is probably your best route.
With that in mind, there’s a couple things to note: She’d be defying the single most powerful political organization in Europe at the time, and would probably be engaging in activity she’d been taught was “evil” her entire life. Getting exposed would be incredibly dangerous to her and she’d need to build up a powerbase that would stand by (or behind) her when her gender was revealed.
Okay, let’s talk about the time travel issues before we get into the issues with mixing those and martial arts.
The first is viral. You have no acquired immunity to small pox, and neither do I. Cited as the single greatest achievement in human history, we effectively wiped it out in the 20th century. No one alive today under the age of about 50 has any immunity. Your main character just introduced a fresh strain into the 1980s… that’s a minor viral apocalypse right there. To say nothing of anything virus or bacteria she’s carrying that modern medicine has never seen.
Also, she doesn’t speak English. No, really, she wouldn’t. She’d speak Middle English, which marked the introduction of French into the English language, but, she’d be incomprehensible to someone in modern day, outside of someone with a doctorate in English lit. And of course, any modern speaker would be incomprehensible to her. If you want to get an idea of what her language would look like, Chaucer isn’t a bad place to start.
So your character would need to learn a new language everywhere she went.
Third issue with time travel is culture shock. She needs to jump into the distant future, decide, “no, wait, I understand these car things” and all the other random insanities we consider mundane. There’s a lot of fodder for humor at the expense of your character here, but honestly, it is a serious issue. Again, your character isn’t stupid, but, at the same time you can’t simply shrug off a thousand years of technological and social advancement in her quest for superpowers.
If you’ve never seen it, watch Farscape. I know, it’s sci-fi and has nothing to do with time travel… most of the time, but John’s constant spaz outs, and the way the rest of the crew view him as slightly defective or insane isn’t that off tone for what you’re character would be facing. Also, seriously, if you haven’t watched it, you need to, if only for Aeryn.
Also, the major thing to take away from Farscape or, even if you don’t watch it, just to understand, your character wouldn’t be stupid. The people around her wouldn’t be stupid. People haven’t mysteriously gotten smarter over time. She’d be uneducated but not stupid.
The fourth issue is one of perspective. In the middle ages it was popular to view the world as fallen. The church certainly capitalized on this, saying sin, and the fall of man was attributable to The Garden of Eden and Eve’s actions therein; this was also what The Church used to justify the misogyny your character would be dealing with on a daily basis. But, there was a real feeling that humanity had fallen from previous golden age. It doesn’t matter if she’d look to Ancient Greece, Rome, or King Arthur, your noble would be more likely to use time travel to go back, looking for some lost mythic era. Rather than looking forward to a world she, by definition, can’t be aware of, and wouldn’t expect to be any better.
Here’s the problem with training on a rapier, she’s using an arming sword: they’re different weapons. They’re used differently, and you can’t swap out and use one like the other. You also can’t use an arming sword like you’d use a longsword or a zweihander. They’re all swords, but they’re all different weapons, with different characteristics. There’s some overlap in how some of them are used, but the rapier is one of the most specialized swords out there, so that would literally be wasted training.
Even if whatever system she’s using doesn’t consider the rapier technology, and no mistake, it is technology. It wouldn’t do her much good in the eleventh century. You see, starting with the introduction of the gun, in European combat, armor initially increased in weight to deal with incoming fire, but over time, as firearms improved, armor shifted towards lighter more mobile designs. The rapier evolved to exploit the vulnerabilities of lighter looser plates and the transition to more mobile combat forms, which your character wouldn’t be facing after she jumped back home.
The same thing is true of unarmed forms. Modern Muay Thai isn’t the worst possible martial art to take into an eleventh century European battlefield, but it’s close.
Martial artists will, inevitably get asked what the “best” martial art is. The smart (and/or honest) ones will respond with something along the lines of, “there isn’t one,” or “they all have something to offer.”
It’s probably better to think of unarmed forms as a toolbox for solving combat problems. Some deal with certain circumstances better than others. The forms that will handle a given problem best are usually ones that were built to deal with that specific situation.
That is to say, Muay Thai isn’t built to deal with armored opponents. In some cases you could kludge it to deal with one in an emergency, or you could improvise. But, the form itself isn’t really going to help you.
Muay Thai is built for dealing with single unarmored, unarmed opponents, and under those circumstances it excels. But, that’s not what your character will face on an open battlefield.
Ironically, none of the modern martial forms are really designed to deal with someone in plate armor. It’s not a situation that we have to face anymore, so none of the prominent styles have a specific, “oh, this is what you do when dealing with someone wrapped up in enough steel to make a ‘57 Chevy.”
Some of the reconstructed European styles have techniques that deal with plate, and it’s a safe bet the historical styles did too. Europe had a terrible habit of tossing martial arts on the pyre once they’d outlived their usefulness. It’s inconvenient for us, and means your character’s better off looking for hand to hand techniques in her own era, rather than time traveling for them.
And here’s the real reason I just spent the last twelve-hundred words taking your teeth out: Your character doesn’t need to go time traveling for superpowers in order to fight alongside the men in her era. She can do that fine on her own, without any special advantages. Either your story is about a time traveler, or your story is about a woman who ran away from home and went to war because it’s what she believed in. But, saying she needs superpowers to be on par with a conscript is saying, “my character’s inherently flawed because she’s a girl” and, I’m sorry, but, that is just bullshit.
There’s this horrible trend in writing female characters, where the author goes hunting for some super special way to say, “no, really, my character has superpowers that bring her up to par with the boys.” You don’t need superpowers for that. Superpowers are about being more than anyone else, not about being “just about equal” to unpowered men.