Why did a William the Conqueror, a Frenchman, become the King of England?

In the 1050s and early 1060s, William became a contender for the throne of England held by the childless Edward the Confessor, his first cousin once removed. There were other potential claimants, including the powerful English earl Harold Godwinson, whom Edward named as king on his deathbed in January 1066. Arguing that Edward had previously promised the throne to him and that Harold had sworn to support his claim, William built a large fleet and invaded England in September 1066. He decisively defeated and killed Harold at the Battle of Hastings on 14 October 1066. After further military efforts, William was crowned king on Christmas Day, 1066, in London. He made arrangements for the governance of England in early 1067 before returning to Normandy. Several unsuccessful rebellions followed, but William's hold was mostly secure on England by 1075, allowing him to spend the greater part of his reign in continental Europe.

William the Conqueror was from Normandy, located in northwest France. The King of England in the late 1050s and early 1060s was Edward the Confessor. Edward was William's cousin. Since Edward was childless, there were multiple people who claimed that they were the rightful heir and should become king. These conflicting claims gave rise to armed conflict. William invaded England, where he won the Battle of Hastings, defeating earl Harold Godwinson. A number of battles followed, but William became King of England late in 1066. He dealt with multiple rebellions over the next decade, but retained his power. Ultimately he was able to return to Normandy and rule England from there.