I'll be transiting through CDG with my cat in a hand carrier. Anyone know if there are rules against bringing in-cabin pets into the AF lounges?

A second bonus question: Anyone familiar with transiting from one non-Schengen flight to another with an AF in-cabin pet at CDG? Sans animal. my experience is one passes through passenger screening on an I-I connection. My concern is either whether those CDG security folks will ask for EU documentation or if AF counter staff will demand it before I board my flight going to CDG. (I know the US documentation restrictions are much more lax than the EU).