Migration between countries has happened for centuries. When the Normans conquered England they also inherited control of its wealth and natural mineral resources. When the Norman army came over with William, a lot of them would have been rewarded with land and property for their support, and would have settled in this new country.
Domesday Book provides key evidence that many Normans migrated over to England in the medieval times, the large medieval manuscript records the names of all those who owned land at the time of King Edward’s death in January 1066, and again when the survey that produced the Book was finished in 1086.
It demonstrated the change from Anglo to French immigrant landowners, demonstrating the Norman French migration across to England to start a new life. Many people started to live lives on both sides of the Channel, crossing the sea when they needed to. William the Conqueror himself was one of these. See more on the Domesday Book