...No? Nations are pretty wide things, and the Franks go a long way back and covered an even wider area than modern France.
Do you have a source on its founder Hugh Capet not being of Frankish heritage? His overall dynasty, though not exact Salic law bloodline (a practice of Frankish origin), ruled from 987 to 1792. From the moment it ceased being "West Francia" to the French Revolution.
The Ancien Regime's centralization you seem to be criticizing was closer to the Kingdom of France's end than its start and saw little change in what nationality comprised the ruling class. If anything the management became more French rather than less with the promotion of bureaucrats from lower and consequently more localized classes to replace the aristocrats with far more frequent and distant outbreeding and education opportunities.
There is no "natural" qualifier, nor are nations clean ethnic groups, and customary variance is routine. Nobody would ever consider Latin America's cultural and political situation remotely organic development and the bloodlines are only sporadically and partially mixed, yet nonetheless there exists a clear Mexican national identity. To say nothing of the incredibly long series of migration policies, population controls, and internal administrative border changes that created Ukraine.
What about the Parisian culture disqualifies it from the broad category of "French" that spans well over a thousand years? Those it impressed its dialect and cultural specifics on were mostly already mutually intelligible and identified themselves as fellow countrymen to a quite significant extent.
I do. Franks and french have nothing to do with each others, They are gallic latin hybrid dominant.
Capet was Only King of the Frank "
Rex Francorum" the idea of France did not existed at all under his time in 1000, if titles are you main interest. It only emerged on paper centuries later in the XII century. The usage of French as administrative language (or whatever it look like back then) emerged in the XVI century.
Capet was not the ancestor of the people. Franks were a small minority of invaders. They had no major impact on the demographic, beyond being the nobility.
French identity for the common people is a post 1789 construct of the French Revolution.
The increase of a bureaucratic class, is call a State. Hyper-centralized around the Parisian egality based familial system, from the famous jealousy, universalism and equalitarianism of the core french culture.
Emmanuel Todd work on Family model do show the extreme variety of familial structure. (following Strauss on that) on the territory.
It is pointless to speak of it, but french identity was forged by the Republican and Royal administration of the XIX century and late XVIII century. France is at core a continental colony. Corsican, Burgundians, Britons, Aquitans, Savoy, whatever have been colonized. Savoy beg the Swiss in the XIX century to take them in, instead of the French. Quite official story. denied to avoid a war. They got a very free and very fair vote to join the Glorious III Napoleonic Empire and subsequent Republic.
There is a French academia about it, by leftist mostly, but true enough, it is a State shaping the territories under his control, not the territories shaping the state. a Soviet vision of the world.
Ukrainians ethnic-cultural-familial do exist as the main population of Ukraine separated from Russians if with significant minorities, same as 1930 Poland, and proximities.
To each his definition of Nation i guess. I have the German (also Japanese, Korean, Israeli= historical one. Unity of Language, culture, blood and past. It imply some amount of (fictional) uniformity. it is made by the family inheritance not by the government service.
Nation is not Citizenship either, on the legal side.
The Official definition on Nation for France and Belgium (caugh) is willingness to live together and obey the law.
It does not constitute nation but simply servitude. The Overbearing State in France is a result of natural secessionist leaning of fringe territories.
I don't know Mexico, never been there. Europe, From East to West i know better.