The thing to remember is that these are arbitrary labels that we are using to describe our perception of the collective style of a whole continent or city.
Just imagine if some European were trying to describe "American Chic" or New York Chic". Pretty difficult to characterize, isn't it?
That being said, I'll try to describe my take on Parisian Chic, since I spend a lot of time there. I can't speak for all of Europe!
I would use many of the same descriptions that nancylee used in her post.
Neutrals: beige, brown, camel, black
Solid colors, very few patterns, but great attention to detail and interesting style elements
LOTS of scarves, tied all sorts of ways, looking "effortless"
Hair is less perfect than in the US, often looking slightly messy, in an "artless" way
Meticulous skin care, subtle makeup.
Stylish Parisiennes tend to be quite slender
Lots of smoking (yuck!)
I have to disagree about no heels: I notice quite a mixture. Certainly for walking many women wear flats or low heels, but I see plenty of higher heels, particularly in the evenings.
Great handbags and boots
Just one person's observations.