If you're going up against any nation that doesn't have the ability to sink an aircraft carrier (which is almost every nation in the world) they are very far indeed from obsolete.
[0] So long as you have a serious logistics chain and serious support vessels including protective warships; if all you actually have is one aircraft carrier, you're going to find it pretty useless for long-term power projection.
The defense against Russia and China is the nuclear deterrent. There is not going to be any direct war between France (or the West for that matter) and Russia/China.
https://www.jewishpress.com/indepth/opinions/firefly-israels...
I've heard people say that this obsoletes large surface vessels and even manned fighters.
They’re used to project power indirectly, by proxy wars in less developed countries (and sometimes for direct wars with them, without proxy of other empires, at least at start).