I never really understood why the tapestry is considered French. The Norman aristocracy at the time did not take orders from the French crown.
I think calling the Norman invasion French was a simplification for children which outgrew its intended audience. They did absorb some of the French (Flemish) aristocracy by marriage and alliance though, and the Flemish played a large part of the colonization of Britain. I've also heard people refer to the subsequent invasions of Ireland and Wales as 'English'.
Humm, honest question, why did the royals from the Norman conquest on start speaking french?
I guess the Normans while not being "ethnically" Frank or Gallic at the time, had already been absorbed into "Frank Culture". They were also loose vassals to the king of France at the time as I recollect.
"Ah, l'Angleterre, cette colonie française qui a mal tourné." - G. Clémenceau
--Edited for clarity