[mousquet]

Of course as long as the country is a more or less sovereign nation, Paris obviously remains the capital.
But I'll play the game for 2 seconds, for fun.

Clermont is definitely way too small and nothing much institutional. We'd have to at least triple the size of it to host the mammoth (the national administration) over there. And it would cost billions of euros of enhanced infrastructures to have it easily accessible from any region of mainland France. Those billions of euros we don't own, unfortunately.

Most obvious and convenient pick would be Lyon in my opinion, guessing the French wouldn't grumble too much if they ever had to acknowledge it as a new capital. Though I wouldn't bet locals themselves would even be really excited at the idea of the mammoth sitting on their city.

In fact, while it seems totally far fetched these days, in this politically troubled environment, the most likely is still Brussels. That's not even France at all, assumes a European federal government, thus the end of the independent French nation. No doubt we'd grow better off and much more powerful by such a radical option. Just too bad it's still so disturbing to most people. Hell, nationalism is rising again just about everywhere, and not just over Europe.