The consequences of this aren't isolated to the British Isles though, I would like to point out.
Normandy without William the Bastard is bound to be pretty unstable while his boys come of age to take over the duchy. Furthermore, William had had to do a lot of fighting to secure his position and expand his lands (specifically in Maine). Anjou is in no real position to invade right off the bat, but we could see a seizure of control from Flanders, or from William's half-brother, Odo. Honestly, I think it is likely that William's children will have the support of their uncle and grandfather in Flanders, but the nobility of Normandy may not be so supportive either and some might rally behind Odo... and Odo might also try to use William's boys for a future invasion of some sort, since the Norman claim to the English throne isn't just going to go away once Harold wins.
What happens to Normandy is in the air, really, but myself, I don't see it being stable for awhile, which could mean, as Fulc the Black comes into control in Anjou, that Anjou takes control of Normandy, or maybe even forms some kind of an alliance with the Normans with more continentally centered interests (something to do with expanding their lands within France and isolating the Capetians, since the Capetians controlled a sliver of France during the period). Perhaps a Norman dynasty in France?
Still, the most powerful people in France are the dukes of Aquitaine, and that situation is unlikely to change for at least a little while. This surely butterflies the Hundred Years War though, as the ground work for that was laid when William the Bastard became a king, begging the question of England's position when contrasted to France, which was complicated by further intermarriage between the Norman and French nobilities of the time.
The wider effects that this has on history could be very interesting, quite honestly. As I've mentioned earlier, England will almost certainly be a more centralized power, and in the coming decades, barring the possibility of a civil war between Harold's twin sons, it would be ripe to enter the stage of European politics as a major player. You could be looking at a reverse invasion in the ensuing decades, with the English invading Normandy, harrying it, and subjugating the Norman nobility and possibly even replacing them entirely with nobles of their own, a la the Norman invasion of England.
By the way, this also weakens the pope's position in the Church, I think. The pope gave William a papal banner and a ring. Not an enormously significant gesture, BUT, William's victory won the pope SOME brownie points, and it certainly probably won Hildebrand some with his fellow cardinals, which would have lent to his election OTL (if we are disregard stories about his popular election by the Roman people, that is). No Hildebrand means no Gregory VII, which means possibly no Gregorian reforms, which means a possible continuation of the "two swords" doctrine within the Church, allowing for the Holy Roman Emperors to choose the popes. Simony might continue to be the norm for quite some time if Hildebrand never becomes Gregory VII.
Remember that the position of the papacy was in a lot of trouble at the time. Christianity was really nothing more than another arm of various monarchical states, each vying for control of that arm. Many in the clergy wanted reform, and were fighting pretty hard to get it - but it's hard to get when every person you give a banner or a ring or throw your support behind in any way ends up dead/deposed/defeated/humiliated. Without the Gregorian Reforms, Christianity in Europe could look VERY different. In fact, you might see an earlier Reformation, as the corruption of the Church would be difficult to sugarcoat while your bishops continue to double as dukes that war with one another to expand their parishes.