Who backed William of Normandy to become king?

Answer 1

Actual backers of William's invasion included the Pope because of Harold's alleged "oath breaking", but more so because of Harolds attacks on the Church's powere and property.

King Henry I of France, Despite previous actual war between Henry and William, even if the latter became King of England, as Duke of Normandy he was a vassal of the French King. France and England had been on again off again enemies for many years.

Baldwin V, Count of Flanders, William was married to Mathilda, daughter of Baldwin.

Several lords of Britanny who had been allies of William against Henry I.

( It's all complicated, but the old adage sys. "Though he has been my enemy, the enemy of my enemy is my friend.")

Also various and sundry enemies of Harold Godwin's family and allies. Some of them English Exiles.

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After the Conquest and William's coronation there were still Godwins and allies, whose power and lands William gave to his supporters, who rebelled from time to time, It took at least another ten years for the Conquest to finalize. There were several minor and major rebellions against now King William. Some of them by former supporters. Some were supporters in one rebellion but were rebels in another, then switched again. Even the Pope withdrew total support since William did some of the same things concerning the Church as Harold had.And complicated relationships with supporters who were now foreign countries at odds with England and William as its ruler. Especially France, there was the long standing animosity between the countries, but William was still a vassal of France, but that had never been a comfortable relationship either.

Its hard to really identify supporters of William AS king. On Tuesday someone might be, on Wednesday not so much, on Thursday in rebellion, Friday a supporter. Mostly depended on who they were supporting him against.