For something silly and romantic, you could have Billy Bastard not get lucky with that stray arrow hitting Harold in the eye. By most accounts I've heard and read, Harold had completely outmaneuvered the Normans and had the Battle of Hastings in the bag. I mean, even after he got shot, the Saxons only lost because they broke formation once the king wasn't around to keep them in line.
See, William's cavalry had to run up and down a hill all day to throw spears into a shield wall of heavy infantry and they were getting pretty much nowhere and the horses would surely have given out well before Harold's thegns.
So, skimming over the details of the battle a bit, let's say that Harold wins the day and William of Normandy is killed in the fighting. Now, to be sure, a period of rest would be called for for the Saxons, but you can't just pretend you weren't attacked without provocation and with a transparently bullshit cassus belli , can you? I mean, Harold would have to do something, surely?
Now, after fighting off the Norwegians and the Normans twice in the row, I have to imagine that Harold would be practically drowning in prestige at this point so, I was thinking he could do something of a variance on the theme of what William had done. Something along the lines of William attacking under a Papal banner and failing meaning that God had willed him to win.
Anyways, going off of that bit of P.R., he gets into contact with the young king of France (who isn't particularly fond of the Dukes of Normandy, by the way) and proposes that, clearly, William of Normandy's titles were forfeit due to him having defiled a Papal banner. And, of course, who better to get those titles than the one who revealed the Bastard as being the blackguard he was.
Now, this is silly and a huge stretch, but I like silly and a huge stretch. What you would have with this is more or less the same situation as post Norman Conquest Britain OTL so, you could do it this way. If you were filly silly and poetic.