The Kingdom of West Francia was just renamed to Kingdom of France, it had the same capital aswell. Yes, it was a feudal system but it was still part of it.
To me and to many others (including historians), France as its own entity appeared at the Treaty of Verdun. Obviously though, opinions differ about that anyway, historians themselves don't agree with each other.
Some others would say that France goes back to 481 since the Kingdom of the Franks was referred to as "Francia" and in the end, after the Treaty of Verdun when only West Francia remained with the name, it was simply translated from latin "Francia" to french "France". This is actually what we learn at school. Though, actually if we use that option, that would legitimate the natural borders of France which go all the way to the Rhine river.
I have to add that Paris was the capital of the Kingdom of the Franks for the longest time, and it became the capital of West Francia, and then France. Also, for about 300 years, the Kingdom of the Franks was mostly today's France.
Today, half of flanders is French aswell, and has been for a few hundred years now.
I do agree, the Burgundians left some pretty cool stuff here aswell... so did the Spaniards with certain buildings and traditions.
I suppose we could go on about this for hours and we would still see things differently and that's normal. I do respect the Belgians though, I'm from Lille and I spend a lot of time on the other side of the border - afterall we were all into the same *country* at some point :)