Shakespeare is from around the same time period as Rabelais in OP. If you haven't read Hamlet, Othello, King Lear, As You Like It, they also take some getting used to but are worth it in the end.
I don't think that English changed as much, but I could be wrong. Shakespeare's not hard for a modern English reader, given a decent edition with vocabulary hints in the footnotes. I got through most of it as a sophomore.
Spelling fixes feels like an "allowed" cheat though IMHO. You are still with the original. Spelling wasn't very standardised and you want to get the word across. Changing word order and idioms though, then we are veering into "translation" territory.
A good middle point would be Chaucer then who had Middle English vs Beowolf''s Old and Shakespeare's Early Modern. The Canterbury Tales is frequently found in translations now, but that's also due to the lack of spelling standardization until 17th and 18th centuries in addition to just vast vocabulary differences.
There’s got to be a chronological point where older Greek gets much easier, though. Or at least, there was back when Greeks still had to work with katharevousa in school. I learned both Ancient Greek and then, though a year spent in Greece, Modern Greek. When I pick up late Hellenistic literature like Achilles Tatius, I feel like it is activating more the Modern Greek part of my brain than the 5th-century BC Athens part of my brain.
Greek, on the other hand, has lifetimes' worth of good stuff in its ancient forms, and can really reward the time spent in learning to read them.