There is being quite an "historical" discussion about the fact of the Normans being "French" since they brough the "french" culture and language to England that changed the scandanivian and germanic culture and languages that England had experience since the Migration Period .
Normans are more or less portraitd as French since of course Anglo Saxons are the "Tragic Heroic People" as Normans the "the evil orks" and of course part of tradional enemy of England France ironical enought that the tradional English-French Rivalary didnt existed before the Norman Conquest since it because of the Normans that rivalary was created since Normandy already wage several wars with France with conquest of England and rise of rise of Angevids to power that compete in France with House of Capet ; this brough the series of wars that England and France had.
So trully are Normans french? Apart from this I find several reasons why they shoulnt be considered French:
The fact that in this time there was hardly a "French identy" and the nature of French people itself is compex, the Gascons ,the Bretons,the Catalans,The Basque,The Flemish never consider themselfs French there was hardly anyone outside the French Kingmon Royal domains that in what is now France consider themselfs French and not to mention of course the Normans. Another thing particular is the nature of French as people contrary to other european peoples like for example the English the French never had a just one people there was never a French People so to speak but more a various group of peoples under the Isle of France Goverment that have been along history enduring a "Francization ".
Another reason is Normans themselfs a people that never consider themselfs French .
They are descends of Viking raiders of France that settled in Normandy after a "deal" with Kingdmon of France since that time the "settlers" intermarried and incorporated customs,language of local Frankish people but they never lost their identy as people true they were mixture but they were still a people.
Politicaly the Duchy of Normandy was subornited to Kingdmon of France but in pratice it was pretty much independent they wage their own wars (against Brittany for example) and even against their suposed "masters" the Kingdmon of France various times they had their own Law and Soberany.
Linguistically they had their own language the Old Norman that had more than 1000 words of Nordic origin altough was part of langues d'oïl group.