There is a 5 night stopover in CDG on the way back. I should've said "[SOME EVEN LATER DATE]" Sorry if that was unclear. So unless the flight rules allow for an extended stopover, which AF said that they did not, then that doesn't work. It needs to be 3 different segments.
It sounds like you're saying that AF isn't the definitive word on what flights AF can book? And I don't mean website, I mean a phone rep? That's pretty amazing.