If you've ever taken a foreign language course in school and actually tried to use the language you consultatlearned in the actual country, you quickly come to realize there are marked differences. School teachers teach what I call "text-book" language, which is grammatically and structurally correct. It's necessary to do this in school so that the students develop the correct foundations of the language. However, in the real world, people don't speak like they're reading from a textbook. If your only knowledge of french is from textbooks (especially if it's from the 80's as mine was), then it's hard to understand some of the slang and jargon of modern day french.

1 Boquin
In textbooks, the word for "book" is usually "livre", however, the predominant way of saying book in french is un boquin. A way to remember this one is that the Parisian book sellers are called "boquinistes"
2 Qu'est-ce que...
You usually learn that "qu'est-ce que" is used to start a question. But it can also be used to mean "Wow...". Let me give an example. If you heard, "Qu'est-ce qu'elle est belle!" it would be translated as "Wow, she's really beautiful"
3 Moche
To go along with the previous entry, the opposite of beau/belle that you would learn in class would usually be "laid", meaning ugly. "Laid" is a word that is heard far in few between and people usually say "moche" instead.
4 De rien
Almost everyone knows the word "merci" to mean "thank you", but the reply to it is usually too long for most french students to bother. In the classroom, we were instructed to say, "Je t'en prie" or "Je vous en prie", which seemed quite long for "you're welcome". Well, it turns out that the phrase is very formal and is not really used in common day to day language. Instead, "de rien" is used, which is the same as our "don't mention it" or "it was nothing" (literally of nothing). This phrase is also very similar to "de nada" in spanish.
5 Quoi de neuf?
"Comment ça-va?" was probably one of the first phrases I learned. But I quickly found out that again, except for formal use, your average person is going to just say "ça va?", since it understood that you dropped the "comment" from the question. Also, a quick infromal greeting that shares the meaning of "what's new" in english is "qoui de neuf?" (literally, what of new?).
6 Ta gueule
This one I ran across while listening to a lot of french gamers online and is a bit negative. I knew it was offensive somewhat, but couldn't tell exactly what they were saying. Well, turns out, they were telling me to basically "shut up". Whoops; I guess they didn't appreciate it when I kept trying to ask them what they were saying. The literal translation of this phrase means "your gullet" which I found out was short for, "shut your gullet/mouth".
7 Ouais
This is simply a change in pronounciation of the word "oui". Instead of sounding like "we", sometimes french speakers pornounce it like "way"