Think about it. When he was still a human, he talked normally. When he was a frog, suddenly he talked as if he was Shakespeare himself. Why? Obviously Magus's magic had affected him more than just physically. It affected him mentally as well. Somehow the part of his brain that controls speech was warped, allowing an increase in intelligence and hence the ability to use Shakespearian language at will. Now it all makes sense.
Speaking in that sort of archaic dialect doesn't mean he's got a higher intelligence. Heck, I could probably speak like that if I really bent my mind to it, and I know someone who's sixteen and could do that easily. Nor is it really Shakespeare. Shakespeare was 1600s, and has a lot of words and phrases that have lost or altered in meaning. All Frog does is use the archaic pronouns. However, those were in use even until the turn of the 20th century (even later, maybe), so it's not really THAT old a style. In fact, I think he uses very few of the words and, interestingly enough, uses them wrongly sometimes, though I can't remember exactly when. It's not hard, though, to replace you with thou in the subject case, and thee in the object (we still do the same with I and me, though admittedly people do often mix them up these days.) Your becomes thy or thine depending if a vowel follows or not. To here, to there, to where become hither, thither, and hither, while from here, from where, and from there become hence, whence, and thence. There are some other words that have fallen out of use that he makes use of, things like forthwith, etc. that I forget right now. But really, I'm reading a 1903 translation of Lucan's Civil War, and it's written in more archaic a fashion than Frog speaks. Heck, he doesn't even use words like 'wont', which was commonly used back then. I myself probably use more archaic words than Frog in fiction writing - I just don't use those archaic pronouns.