(Edit: this was a response to a discussion in the Writing SE. I tackled the non-grammatical elements for that SE by addressing a modified version of the question to aid translation, "How should one approach creating formal speech for a fantasy novel in English?" It's clearly not as relevant in the English Language & Usage SE, but I'm not going to delete a pertinent and useful answer only because the question was migrated.)
Formality in English
As Cyn hinted in their comment, older speech patterns are not necessarily more formal, as people have always used different registers reflecting their education and social status. Generally in the English-speaking world (and, I imagine, always and everywhere) the nobility and upper classes have been held to higher standards of grammar, rhetoric, and diplomacy, and this dictates what is "formal" at any given point in time. In the UK there's even a deliberately-cultivated upper-class accent (Received Pronunciation, or the Queen's English). Sometimes formality does include antiquated language because there will be preserved, formulaic structures that are retained for the sake of tradition, such as you might find in legal declarations ("Whereas, ... I do hereby declare") or religious ceremonies (wedding vows), but that isn't typical of unscripted speech. Typically as well, there is some conflation of formality with politeness in speech. Note that that doesn't necessarily mean respectful or obsequious speech; it's just that insults and demands are not expressed as directly. (For extreme examples, 19th century social dramas capture this perfectly.)
Mixing English from different time periods
Using EME for one character but contemporary American English (e.g.) for the rest would not convey a different level of formality as much as it would say "this character is 450 years old and from another place". Maybe that works for your character, but you would probably still want to hit that upper-class register in EME.
World-building through dialect choice
One way to help your voicing is to draw a cultural or linguistic analogy from your fantasy world to the English-speaking one. Having a baseline will help you find the right registers for your characters. Decide if it makes sense to use contemporary speech patterns in your world (it's easiest for the readers to understand but harder to shake the cultural baggage), and if not, choose a rough date and region from which to draw your speech patterns, e.g., Victorian England. Your mystical entity can be the only one who sounds like Queen Victoria, and everyone else can sound a bit like Charles Dickens or his characters, depending on their social class or place of origin.
Because dialect and slang can be such immediate tags for culture, many fantasy novels try to create a sense of timelessness by avoiding slang and idiom. Sometimes, to be more true to the way languages work, authors will inject their own slang into the piece as linguistic worldbuilding. Either way you want to do it, less slang is more formal in English.
SE prompted me to edit this answer instead of submitting another one, but here's some info more directly related to handling the grammar:
There's a similar question that popped up asking how to handle writing passages in some form of archaic English (in this case, without doing all the research necessary to get it): Believable but easy archaic English?. The answers include many links to additional resources about how and why to use and fake older versions of English, including pitfalls to avoid. I think these could be helpful to you. My advice: don't try to pass off unresearched superficial differences as authentic; many readers will know it's wrong immediately, particularly if you botch the pronoun cases and verb conjugation.