The papal interdict doesn't seem to have caused any concerns amongst the english. Having a different system of law they well knew that the whole issue of any promise by Harold being broken was irrelevant, as the crown was not his to give. Nor that of Edward the Confessor.
It was the Witangemot who chose the King. Realpolitik ruled and they were likely to choose one who had the power to back it up, frequently the eldest male of the predecessor, but not necessarily.
When Harold died they went for Edgar (who, like Louis, gets left out of lists of english kings) but eventually changed their mind, with a large Norman army on the doorstep, and decided William was just the chap for them.
Had Harold waited to assemble a proper southern army then William would likely have lost. Without his allies and outnumbered he would have had to fight on ground of Harold's choosing or risk Harold ravaging the countryside around William's base and starving him back to Normandy.
Even in OTL William, with his allies, had a very hard time and could easily have lost the battle if english discipline had maintained the shield wall and let William's troops exhaust and waste themselves against it.
No french in the language and the verb at the end of the sentence could stay and english speakers like Yoda could sound.