I tried playing France multiple times and I'm sorry, but you guys didn't manage to convince me their UA is any good. There are some very severe problems with France on Immortal and higher. The biggest of all being Wonders. The theming bonus only applies to Museums (of which France can only get one in the capital) and wonders with a theming bonus. These wonders are the Great Library, Sistine Chapel, Globe Theater, Uffizi, Louvre, Broadway, Sydney Opera House, Oxford University and the Hermitage. The latter two are national wonders so you can always get them, and the GL is a no-go on higher levels (someone once told me "Friends don't let friends build the Great Library"). The problem comes with the other ones, making France a very Wonder-reliant building in a game where on the highest two levels it's next to impossible to get the specific wonders you want. Just in my last game I was trying to build the Sistene Chapel but Dido was just ahead of me, and a spy had informed me Theodora had already started constructing the Globe Theater when I didn't even have the right tech for it. And that's despite me having built the National College. Other cultural civs (Brazil, Byzantines, Celts) can function well with or without wonders, but it's only France that NEEDS these wonders. This puts massive pressure on the capital, which needs to have insane production, but at the same time you also need to keep up with science. Even Sejong the Great's UA at least helps with science generation if you're going for a cultural victory. And then there's also the problem of religion, a problem Boudicca has on lockdown but Napoleon will always struggle with. And in a cultural victory you need religion for some good religious policies as well as the world religion perks later in the game.
So in short, I can see your arguments in favor of France's UA but some attempts to play France prove that its wonder dependency means that at higher levels, France may as well not have its UA.