Edit: I looked this up and found this page: http://brandplucked.webs.com/theeandye.htm
It seems to infer that "thou, thee" etc. are only about distinguishing between singular and plural. There's no mention of them being an informal form, at least not in the King James Bible.
Even more:
"As William Tyndale translated the Bible into English in the early 16th century, he sought to preserve the singular and plural distinctions that he found in his Hebrew and Greek originals. Therefore, he consistently used thou for the singular and ye for the plural regardless of the relative status of the speaker and the addressee. By doing so, he probably saved thou from utter obscurity and gave it an air of solemnity that sharply distinguished it from its original meaning. Tyndale's usage was imitated in the King James Bible, and remained familiar because of that translation."
Then more from Wikipedia - the plot thickens!
"Early English translations of the Bible used thou and never you as the singular second-person pronoun, with the double effect of maintaining thou in usage and also imbuing it with an air of religious solemnity that is antithetical to its former sense of familiarity or disrespect."
Also, apparently French uses the informal (see "toi" in the Lord's Prayer), whereas Dutch uses formal (U/uw).