hckrnws

We have a very loose notion of what's "French".

In particular anything that happened in the vicinity of the current territory will fall into that, even if at that time it was different, or the people ruling over it where under a different crown.

Frontiers always moved a lot, and we came to accept them as pretty vague and sometimes not really relevant.

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'.

The Normans accepted the French king as their ruler, even though their lands were ruled separately.

I've always admired the French kings playing the long-game in this. Step by step, over centuries, the French kings took back more and more land from the Normans until it became completely French and the Normans were absorbed into the French kingdom.

I am not sure that is the relevant criterion. The French king as a primus inter pares noble had initially very limited authority over a very limited area. Basically nothing in France was French then, even though they shared State structure and culture, if not strong, direct, central government power.

And they did not stop at England: https://www.understandingitaly.com/normans-in-italy.html

Would you consider Burgundy at the time part of France?

The tapestry is not considered French