"Most likely, the phrase "Ye Olde" came about for the reason Wolman suggests: people were aware that, in older forms of English, words tended to resemble modern words with the letter "e" tacked onto the end. So the phrase isn't used to copy actual pre-modern English but to evoke pre-modern English."

The actual word "olde" in the, erm, old days, was used more to refer to old people than to evoke a sense of time/place like it is today.

 

(More about the thorn, mentioned later in the above article, over here.)