The Kingdom of France dates to the 9th Century, and unified Frankia to the 5th Century, but at least through the Middle Ages, it seems that "France" remained a rather decentralized concept, and it isn't until the "Ancien Regime", or perhaps even the post-Revolutionary period, that the France can truly be seen as unified in the sense of identity.
Obviously, national identity in of itself is often viewed through the prism of the 19th century, but that isn't what I'm asking about. More about how, between the Treaty of Verdun and ~the end of the 15th Century, France was conceptualized, especially by those who lived within its boundaries.
While I cannot speak very deeply, I can try to address the idea of a shared identity. Shared identities are a product of nation building and very difficult with a multitude of problems such as distance, literacy, and regionalism. In The Story of French by Jean-Benoit Nadeau and Julie Barlow, they state that the precursor of Modern French wasn't spoken much outside of the French court even until the 175th century. Due to regional differences, there were a multitude of version of French, or the language d'oil. So language cannot be easily shared as Well as literature since literacy rates were terrible until the mid 19th. Thus culture is even difficult to tie all of France.
Without the major ties of culture and language, beyond the crown, there is very little to tie France together, except for one thing, religion. For a short time (short for Papal history) the Pope was held in Avignion. Further France was Catholic and held It's Catholic identity until the mid 20th century. The future Marshal Leclerc belonged to a very conservative faction of France (before WW2) that was separate from the Fascists but still clung heavily to The Church. It wasn't until the contemporary era that you see a turn away from religion and more toward Republican idealism.
Sources not mentioned,
Free France's Lion by William Moore
France and the French by Rod Kedward