Can French understand French from the Middle Ages or even later? No. And this is likely the case for all languages.

I am French and have a soft spot for French Middle Ages history and culture (completely amateur interest, and very shallow).

I tried to read MA texts. It is really difficult, and gets a tiny bit easier when you understand the calligraphy. As for the meaning, this is basically a foreign language.

When you know what the text is about, you can work out some words and the meaning of some sentences. But only some, and this some is rather small.

I heard spoken MA French and it is not understandable at all.

Languages change much more than we expect it. My son texted me a moment ago "Oe ptdr g vu". Kudos if you guessed that this is teenage French, and congrats to you understood what he meant (when you are not French and a parent of teenagers:))