early modern english - Why did the personal pronoun "you" "survive" and not the others?

I was just wondering, since we started talking about the Early Modern English Period, for England the period of Renaissance, Shakespeare ....

There were four cases in EMEnglish, thou (Subject case) thee (Object case)
ye (Subject case) you (Object case)

As far as I know "you" was used by lower class speakers to address higher class speakers.
And higher class speakers used thou in return to address lower class speakers (non-reciprocal)

I am not sure about the others but my question is why became the addressing reciprocal (using the same form to address each other) "you".
Why was it the "you" form that "survived" and not any other one?
Was is French influence from Middle English (when the Normans conquered England: has it something to do with the word "vous"?)

Thanks,