I took this routing a few weeks ago, having heard how much better AF's La Premiere is than my usual BA First class. However I made the mistake (referred to above) of booking the A380 and I'm afraid I found the in-flight elements of the journey, and especially the seat and the food and wine choice, inferior to the BA offering.
The situation on the ground, however is quite different. The individual care, including shepherding me to my connecting flights, was extraordinary - BA doesn't even attempt to offer anything comparable. The AF lounge at CDG and the VIP part of the Skyteam lounge at LHR are also far superior to the BA/AA alternatives. At JFK, however, it's a different matter and both BA's Concorde room and AA's flagship lounge and first class dining are better than the strange little room AF uses for its Premiere customers.
Bottom line: if I had to fly this route and all 3 carriers were offering first class at the same price I would probably choose AA. Pre-check at JFK (for me) cancels out the AF escort through the zoo that is T1, and in the end, for me at least, direct flights have to be significantly more rubbish or more expensive than the alternatives before an indirect routing makes sense. Perhaps if I'd known to avoid the A380 I might think differently but my recollection was I would have had to pay more to fly on different flights.