My point being if Normandy is stable enough for them to try again several years later, Harold, having defeated one attempt already, should be prepared for them. It was a close run thing OTL anyway and Harold's men weren't at full capacity or rested having come south straight after defeating Hardrada.
My point is that by that time Saxon/Norsern warfare had been lagging behind the "modern" one. Hardrada had been losing to the Normans in Sicily and Guiscard (couple decades later) will beat the Varyangians in the Battle of Dyrrhachium. Hastings was close as long as the Saxons had been holding a defensive position on the hill but as soon as they tried to attack, they had been massacred. Taking into an account the Norman absolute advantage in cavalry and clear advantage in the archers and the fact that most of the Saxon troops did not suffer from the excessively high discipline sooner or later they'd be provoked into a rash counterattack. Or sooner or later they'd have to leave that hill and march somewhere, which would make them vulnerable.
Actually (and this was discussed extensively on SHM/SHWIF) Harold's victory at Hastings would, in the best case scenario, amount to repelling the Norman attacks with, as a bonus, the Bastard being killed. The Saxon infantrymen could not successfully pursue the cavalry and one of William's subordinates would probably end up acting as a representative of his heir. The Normans retain freedom of operation and sooner or later the Saxons are going to run out of the convenient hills (pretty much as eventually happened with the Flemish at Rosebeke).
The whole thing continues for a longer time but Saxon England offers a lot of loot so there would be plenty of enthusiasts in Normandy (as I already said, it looks like the demographic situation among the military class in the Duchy was quite explosive).