England had been invaded by Angles, Saxons, Danes and Vikings before. And the last successful invasion of England was made by Normans.
England was the perfect example that you could see feudal system. All the lands are the property of King and Baron's hold lands in the name of King. Under the Barons there were small elites, knights, who were not noble birth. The other people, serfs, were not free, they had to take permission to marry or move. Though all of the England was the property of King and making a law was just under the King's authority theoretically, Kings could only make laws which would be obeyed by Barons voluntarily. There was not any written Law which was valid all around the England such as Roman Civil Law. Barons were responsible from their lands and laws were different. I mean there were kings to maintain harmony between barons and if harmony could not be kept there would be rebellion.
King Edward the Confessor who was the last king of house of Wessex died in 1066 and the mythological Golden Age of England end. There was not any successor behind King Edward and the most powerful baron Harold Godwinsson whose sister was Edward's wife, claimed that King Edward named him as his successor before his death. However, unexpected claim rose across the English Channel from Normandy where Edward had spent 30 years and been influenced by Norman society. Duke William of Normandy claimed that Edward had named him as successor many years ago.
There were two opposite barons one of them is descendant of Vikings and the other is Norman. Since all of information we can reach is Norman sources we do not know however, Pope had supported William and it encouraged the barons who lived in northern Normandy.
Though William planned to land Isle of Wight poor Norman navigation ability led them to land Pevensey. On the other hand Harold occupied Senlac Hill and began to wait William's army.
Let look to both armies. Harold army's (7000 men) main force was housecarls who used Viking long-shafted axes. They were powerful unit however their support were fyrd, the militia. These were men who had to participate army for a certain time. Harold did not have any archer or mounted units.
William's army's (10000 men) main force was Norman Knights who were destructive force with their heavy weapons. They could stand on their horses with help of stirrups and use weapons. Archers and milita were supporting units.
Though it seems like William's army is more powerful with different kinds of units, he did not have any chance to use his cavalry while Harold army stand on the top of hill and archer could not be effective. So he had to pull Harold next to his army.
Battle was started with Norman archers as usual. However that was not effective as expected. Then William ordered assault to milita. However, position of Harold's army was very advantageous and militia was forced back by lines of Harold's army. Few troops followed militia and these were killed by Normans in open field. Everything was going on as favour of Harold. Norman's were below the hill and there was a rumor about the death of William. William took of his helmet and ordered the second assault to his militia, soldiers who saw William attacked to lines of Harold's army again and the result was same again. There was a slight difference this time nearly all of fyrd followed Norman militia. There were no defensive shield on the top of the Senlac Hill and Norman Knights were not merciful to fyrd who followed militia. Battle was on the ground in the end as William expect. Heavy cavalry smashed all of militia and some housecarls. At the same time archer began to send their arrows. One of them hit Harold and this was the end of army. They divided and before night fall the last successful conquest of England was over.
All of England was lying in front of William and he walked into London with his army.
The Norman Conquest had changed the England. Norman feudal system was combined by England's. England was like a confederation before the invasion, there were Wessex, Essex, Sussex, Kent etc. and government of England became more centralized after it. Though Kings should been supported by Barons still, Kings rights opened road to absolute monarchy which would be tried by King John and lasted by Magna Carta in the future.
It should not be missed that invasion not made by Kingdom of France. It was the Duchy of Normandy which was founded by Viking Rollo as a result of his defeat to King of France and converting to Christianity.