In English, we have several similar words that are derived from this French meaning (putrid is an example). Both words are related to Latin "putere" meaning "to stink". The ultimate root of these words is the Proto-Indo-European root word *pu- "to rot, stink" [1].

It is not clear if the current meaning of the term pee-yoo is derived from this Indo-European root. The first Oxford English Dictionary entry is in 1604, where it shows up with several different spellings: pue, peuh, peugh, pyoo, and pew [2]. The "stretching" of the word into two syllables must have happened sometime later.

[1] http://www.etymonline.com/index.php?term=putrid

[2] http://www.grammarphobia.com/blog/2010/08/on-the-scent.html

In the US saying "Peee Yooo" is often times combined with holding your nose. Sometimes each word is stretched for dramatic effect "Peeeeeuuueeee Yoooooooooo!"

It's somewhat of a children's expression for "that stinks", although adults use it to be funny.