Harold might have sworn an Oath to William of Normandy and went on a military campaign with him, however the actual reason for Harold's visit is still unclear
In the English sources, Harold still swore the oath to support William's claim, but it was not the reason for visiting Normandy - some argue William forced him to do it
For example, the Bayeux Tapestry shows Harold wearing an oath to William, but this was ordered by William who wanted to present himself as the rightful king
King of England since 1042, his father was the Anglo-Saxon king Aethelred, his mother was a daughter of the Duke of Normandy and he was raised in Normandy