Complex question. Lutetia was the capital of one of the provinces of transalpine gaul (tota gallia divisum est....or something like that.). The kings lands in france (the Ile de France) were centred around paris, so it could have been said to be the capital since the fall of the merovingian dynasty, but the actual area ruled by the kings was nowhere near the area of france. The restof it was ours. Sorry, I seem to be rambling. I would take a guess at around 960 but will get back to you. Perhaps there is a friendly historian out there with a better answer?