Why do we say "Ye Olde" something-or-other when we want to sound Old English? According to the history of the term, it was never pronounced that way! Minute Physics explains in a hurry, even though the history of language has little to do with physics. -via Geekosystem
Firstly, there is no such word as "abbreved".
"Neanderthal" dates to 1860-1865, way after the use of the letter thorn had fallen by the wayside. It is also not French, it's German.
There are actually TWO words spelled "ye". The one means "thou" and is indeed pronounced "yee".
The other is the old spelling of "the", was originally pronounced "the" and now pronounced "yee" by almost everybody.