Robert Graves claimed that in his novel about the wife of Milton, he used no words that were not in current usage when his characters were alive.
It’s a splendid Gravesian maneuver. Who’s going to sit there with the OED and check every word? And even if you did, and found some evidence to challenge his claim, I suspect Graves’ ghost would come back and argue that the OED was wrong and he knew better. This was the man who delighted in proving that the details in the I Claudius novels could all be substantiated.
So how do historical characters speak? If you’re really worried about this then, since we know both Godgifu and Leofric spoke Old English, it would be theoretically possible to write their dialogue in that language. Except my OE grammar isn’t that good. But even if it was, who else would read it? And what would be the point?
There are popular routes to follow. Not OE, ME or NE but PHS-‘Pseudo Historical speak’. Throw in some thee and thous, a few God Wot’s and By our Lady’s, and someone somewhere will think you’re recreating the sound of a person in the past talking.
My problem is I wouldn’t be that someone. If you read any Middle English, or even just Shakespeare, neither sounds like PHS. And there’s a pedantic presence (come to think of it, he looks a bit like Graves), that reaches for the OED, or something like Crystal’s “Shakespeare’s Words’ and wants to point out that thee and thou not only have grammatical meanings, but also shades of social meaning, and most “pseudo-historical” misses both.
The other PHS move is to rupture the syntax: God’s Bones and teeth and toenails, knowest thou not, thou fiend most foul, Lady Digberry my good lady is to be my affianced, by our Lady ?
Even Joyce, in the Oxen of the Sun, mangles the ME bits. Graves was a stickler for detail. But even he doesn't make Claudius speak English in Latin word order.
No, the solution I think is to ignore the question. Or to say, you don't even bother trying. Since I am writing in Modern English (NE), my character will sound like they are speaking naturally in Modern English. If Peeping Tom swore in ME, then he can swear in NE. But he’ll swear like a modern person, not by god’s bits.
The historical background, where possible, functional, or necessary, will be accurate.