I thought the Angles were there. It was the Saxons that came later. I think some of the Angles then migrated to the French coast.
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England was invaded in the 400's AD by three tribes from Northern Germany: the Angles, Saxons and Jutes.
England was raided and settled from the north by the Vikings in the 800-900's.
One Viking group had settled in Normandy France by 1000 AD. In 1066 Normandy invaded England. That was the Norman invasion. These folk took over the rule of England from the saxon kings.
In the 1600's English royals mixed with Scottish nobility and in the early 1800's English royals mixed with German nobility from Hanover.
When the Anglo-Saxon invasion came, it was sometimes brutal. Think Americans taking land from the Indians. Many Britains chose to sail to the continent to join their Celtic pals in what is now France, but which at that time was Gaul. Gaul was also a Celtic land, and the Britains would have been at home there. So many British people moved to the Gallic coast that it came to be known as Brittany. Until recent times, the rural parts of Brittany still had dialects reltated to the celtic language spoken in Britain before the Anglo-Saxon invasion.
France did not come into existence until Frankish invasions that took over the whole country, and melded a Celtic land with a Germanic one. Franks were Germans.
Normandy did not exist until a Viking invasion that took over that part of France around 900 or so. Normans were Norsemen who liked the lifestyle in France, and chose to stay. They kicked out the local nobles, learned French, but still had a bit of Viking in them when, in 1066, they invaded the Isle of Britain and toppled the English kingdom on that Island.
This is a very brief summary. I hope it helps.