loyal readerships ≠ royal leadership (but it was a fun misread)

About the discussion at hand, it would be interesting to compare contemporary texts. For example, the Normans in Italy were compared by the Byzantines, as far as I can remember, with their own Northmen (the various mercenaries and settlements in Eastern Europe), possibly because of the name; but the also Byzantine Alexiad simply calls them Keltoi, "Gauls/Celts". The Normans spoke French (oil), in a local version, like not having the c- > ch change (which doesn't really mean too much, since local variation will always exist). But I don't know about their everyday customs; I expect the populace to have retained their old (romance) culture, and the nobility to have a few Northern habits.

And England should also not have existed, by royal style, until 1154. I wonder what William conquered, then?

From my point of view, it makes no sense to try and understand when people started use "France", because it becomes a mess from it being an English word. Francia was used since the "beginning", since Chlovis I (466 511), and referred to all of the territories held by his Franks. When the Frankish Empire broke up, there were definitions like "Francia occidentalis" opposed to "Francia orientalis". When the name Francia orientalis became disused, the French state was referred to as simply Francia. I assume that Anglia also existed as a concept for a long time before it was adopted by the king.

In general, while being powerful, litigious, and as independent as they could get away with (so, a lot), the vassals of the King of France well very well aware of being his vassals and of the reciprocal obligations. Respecting them, that was another matter.

I personally wouldn't call William's men Frenchmen or Franks, if only to avoid confusion (although it would be interesting to check out what medieval sources called them; translations tend to change such names into something the readers can understand). In general, this kind of definitions can be a mess. Isidore of Seville called the inhabitants of the Visigothic Kingdom "Goths", in spite of them being essentially the same people as before the Goths got there, and keeping their earlier language and religion.

I don't know how widespread a feeling of loyalty towards the king was. I tried searching for prayers for him in liturgy, but I couldn't get earlier than Philippe le Bel.