Sorry, but this is a pretty surface-level take. The Shakespearean plays and the French language are vessels for other skills. Literary criticism, argumentation, media literacy, acculturation to a shared literary canon, and even just how to talk about books are all additional aims to using Shakespeare in an English class, beyond "learn this book you hate". A good English class can focus on these skills with any content, but Shakespeare is used for his contributions to the English language and literature in addition to his privileged place in culture (a valid avenue for argument).

The targeted plays might not be every student's cup of tea, but some students will love Shakespeare and hate your favorite book. As long as the classroom is used as a social learning space, there will need to be shared central content used as a medium for the skills--which are more important and enduring than the exact content of the plays. It's the same for the French grammar you don't remember but which gave you the rudimentary skills to study another language more effectively.