A French leave refers to the act of leaving a party without bidding farewell to -- and thereby not disturbing -- the host.
In American culture it's considered rude to leave a party without saying goodbye, but -- in my mind -- it's much more rude to create a scene over the fact that you're leaving; air kisses and phony sentiments are not for me!
On this subject I am unapologetic.
I think that the French -- and dogs -- got it right. Dogs, you ask? Yup, in the wonderful world of canines there are no goodbyes, only hellos!