Sometimes it's more subtle than false friends. I've learnt to be careful with <em>n'importe quoi. </em>It does mean 'anything', but often in a negative way.
For example, when a host asks you about what you can eat or want to eat, a polite anglophone guest might say that they'll be happy to eat 'anything'. Said in a reassuring tone, this seems a good thing in English: you're showing that you're a good guest by not being picky or demanding. Translate it into French, and <em>Je mange n'importe quoi</em> comes out as more like, "Don't worry about me! I'll eat any old cr*p!"
And then you wonder why you're not invited back :)