Normans were Vikings who settled in France from about the 9th Century onwards.The French King accepted their control of Normandy in 911 and gave them the titles Dukes of Normandy.
Gradually, they became integrated with the local French, and practised a particularly ruthless form of feudalism that enabled them to turn out well trained, well equipped, fearless warriors.
They (not France) conquered England and parts of Ireland, Scotland, Sicily and at one time they actually ran the Christian kingdom in the Holy land.
Quite a few Norman (not French) castles still survive today....The Tower of London, Windsor Castle, Warwick, Chester etc etc.
Everyone knows that the plante genet (broom flower) dynasty was French, but they pretty well fizzled out in a blink of England's long history, and their DNA certainly didn't permeate down as far as the aforementioned 99.5% of us.
I would say that we (British) have infiltrated French life FAR more than they have ours. Just look at how many of us now live in the Dordogne, or the Poiteau-Charente, not to mention Brittany.
And as for being passé.....the ineffectual plante genet lot were done and gone over 600 YEARS AGO!
How much more passé can you get? (Insert smiley face here )