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.
