Obviously. When established as a duchy, it owed fealty to the King of France. Then, in 1066, the Duke of Normandy became King of England. However, when he died in 1087, he gave England and Normandy to different sons of his. While they would later become connected again, Normandy was still separate in 1100, and owed fealty specifically to the French king.
This sounds like a later era than 1100. The first medieval universities were only just getting started. Paris would’ve been an attractive location for schooling, though their university was yet to be chartered; the English nobility, being largely derived from the Norman conquerors of 1066, had close ties with France. Nobody would’ve been going anywhere to become a lawyer in 1100; it would be later in the middle ages that law codes were more in place. People would be going to Rome for pilgrimages, being a holy site, and being the site of the Pope. Hence, going to Rome for religious reasons, which was what I said.
People talked about homosexual acts rather than a homosexual orientation. The terminology they used was sodomy, which refers to specific acts, which can be performed by a man and a woman as well. The church disapproval was against this, and not against any kind of attraction itself.
Sexual morality was entirely a church matter in 1100 England. No king would bother with it; the church would judge any such cases. That was true all the way until the 1533 law that I mentioned, specifically the Buggery Act. Before that, there was no risk of execution for same-sex relations in England. The king was not an absolute monarch, either.
As an example, while it’s debated whether Richard the Lionheart was involved with other men or not, we can at least note that he did penance for “the sin of sodom” (which he could’ve performed with other men or with women) and… that was it. That was enough to clear him. That’s the penalty for sodomy in 1100. He’s also known to have shared a bed in his youth with Phillippe of France (later king), which didn’t necessarily imply anything sexual; what it does imply is that close intimacy between men was generally socially improved of. Under such circumstances, male couples could have public displays of affection and everything as long as they’d stay discreet about the actual nature of their relationship.
As for lesbians, people weren’t even really talking about that (or, at least, the people who were writing the records). They’d be even less likely to suffer difficulties for their relationships. The main issue would be pressure for marriage.
Things did get worse a few centuries later. And laws would exist in some other parts of Europe. Medieval Europe varied a lot.
Additionally, in this case, having a legal rather than ecclesiastical ban is the anachronism. This is a case where making it a little more open would be more accurate, not a matter of altering history to fit modern norms at all! Anybody could be in a socially-disapproved relationship, male-male, male-female, female-female, facing roughly the same problems if it’s outside of marriage. (Even a little less problem, in that pregnancy was not a risk.)
Why does so much medieval historical fiction feel like it needs to portray things as having been worse for gay people than they actually were?
However…
In that case, you may be better off dispensing with the historical setting. If this is really the way you want your story set up, then having it be set in your own fictional setting would mean that you’re not misrepresenting history.
