‘Frenssh’ as it was ‘spak’ in medieval England

"Slant rhymes" like this have been used throughout history. Shakespeare is known to have used them in some places: some of his rhymes aren't consistent through his works.

It does help that sound change isn't arbitrary. When one sound changes, other sounds change as well. An entire category of consonants may lose or gain voicing, or shift in point of articulation. When one vowel changes to another, a lot of words can become homonyms, so usually every single vowel changes at once. These are called Chain Shifts:

https://en.wikipedia.org/wiki/Chain_shift

So a single instance of a rhyme is a weak piece of evidence, but when you take into account all of the texts at the time -- and the texts from surrounding times, both before and after -- you can make a good hypothesis. That hypothesis can then be tested against future discoveries, and modify as appropriate.

That's why all Proto Indo European reconstructions are marked with an * to say "We've never actually heard this word so we don't know if anybody ever said it". They're aware that all hypotheses are tentative. But that's how progress is made.

Of course, it's all pretty pedantic, given we are talking about names in Old English and Old French, and an Old French name is as removed from a modern French one as it is from an Old English one, so naming these figures with their modern equivalents for the modern reader makes sense too.

I just like reminding myself these early English monarchs were not, in fact, English, and would not be, and would not consider themselves as such, for a while. It also emphasizes how much of a relatively unimportant adjunct of their French lands the Angevins considered England.

WS Allen in his book, Vox Latina, actually explains how Latin might have been pronounced in the Roman period. Interestingly his theories have universal acceptance today.

Rhyming lines in poetry are a great way to constrain what the various phonemes were. The meter is also a great way to back out what sounds were silent and which were not. (Speaking of which I disagree with the video's choice to pronounce a lot of the final "-e"s in words; that's a trait of early Middle English that was already on its way out by the time of Chaucer and its pretty clear from certain rhyme choices that it's silent in a lot of Skelton's words: see how e.g. Skelton rhymes "Jerusalem" with "creme" and how everything is nice iambs, unless you start pronouncing "-e"s everywhere).

500 years is also within a time horizon where you can get pretty reliable internal reconstruction clues (examining inconsistencies in modern English and thinking about what common features might have led to those inconsistencies) to try to get a better grasp of the phonemic inventory of a language.

Spelling also is a great clue into what the phonemes of the language were (although this is complicated by digraphs and trigraphs).

Then you can use a variety of methods to try to get an idea of what the phonetic realizations of those phonemes were. In this poem in particular we have English words rhymed with foreign words which is a great clue. You can also compare different dialects of English to try to figure out what the original sound is of a word that has now fractured into many different pronunciations.

And of course you can examine what people of the time say about the pronunciation of their own language (this is how we e.g. are pretty confident in r being a trill or a tap, based on descriptions from both domestic and foreign speakers, see e.g. https://english.stackexchange.com/questions/298566/why-and-w... for a great summary of some of the evidence).

All in all it's kind of like playing a game of Sudoku. Rhyming and other clues can set up a set of relationships among different sounds and what would seem like an otherwise sparse set of clues (a comment by some writer here, a common misspelling there, some translation here) can cause cascades of phonetic realizations of different phonemes that magnify the impact of those clues.

And the sanity check to make sure that all this makes sense is being able to provide reconstructed sounds that are consistent with new descriptions, rhyming patterns, and foreign transcriptions as new evidence rolls in over time.

[1] incidentally, one does sometimes hear things like "er ist am kommen" (lit. "he is at coming"). Is this a new development, and is it a borrowing from English?

It's definitely worth reading through the top questions on those two stacks, but sadly it's not an activity that will occupy you for very long.