If I remember correctly, the Focal Aria 936 have vented ports, one of which is located under the speaker cabinet ... correct? I spent an afternoon auditioning those speakers several years ago in a sound room that was a little larger than yours (i.e. basically a 17' or 18' square with 7.5' ceiling), had minimal room treatment, dropped panel non-metal (probably fiberglass) ceiling tiles and thin builder's grade wall-to-wall carpeting. They were powered by a MAC MA5200, then a similar Luxman integrated and fed some pristine vinyl through a Rega P3 & Ortofon 2M Blue. Listened to some of my test CDs, as well. In that particular room, the Focal were positioned with their backs (not baffles) a good 2.5' to 3' from the wall behind them and separated from each other by around 8' or 9'. My ears fell in love with those speakers!
How close to the wall in your room do you need to position your Focal to get the sound you prefer? Is your room strictly rectangular? Windows? How many? Where? Any behind the listening position? How much empty space is there behind the listening position? What's under your vinyl flooring? Plywood subfloor? Concrete? Is the ceiling drywall or something else? Does it have beams? Is there more than one egress or opening in the room? Are the walls drywall? How much and what kind of furniture do you have in the room? Stuffed? Minimal furnishings? Large bookcases?
I know! I know! Lots of questions! However, as some have alluded to here, all variables to consider because a sound room is as important as the components you put in it. There is such a thing as overkill when it comes to speakers and power sources for any given sound room and too little oomph. As for most things related to audiophile sound fidelity, matching components is important, and the sound room is all too often left out of that equation.
I am certainly no expert when it comes to sound room design. However, from a practical point of view of having had different kinds of sound systems in many different kinds & sizes of sound rooms, per se, I would think twice about putting down wall-to-wall carpeting. I recently got rid of my wall-to-wall carpeting and discovered there was antique type tongue & groove wide pine flooring underneath. So, I had that refinished and listened to my system for a while with the bare wood floor. Later, for aesthetic reasons, I put down a couple large Persian rugs and couldn't be more pleased with the improved sound fidelity over the wall-to-wall carpeting. My sound room (i.e. living room), however, is larger than yours and has a higher ceiling. So, I guess I'm seconding or thirding or whatever the motion to experiment a bit, first, before going whole hog and putting down wall-to-wall carpeting. Use some rugs or get some remnants to carpet the whole room and try that. Then, use some area rugs in front of the speakers, etc. I think that might give you a pretty good idea of where to go from there. You may find you don't need any sophisticated room treatment(s) at all, and simple window curtains or drapes or a strategically placed bookcase might suffice.
Good Luck!