In this event I imagine the witenagamot would simply elect Harold Godwinson King anyway. Fulk of Mantes wouldn't be in any position to enforce his claim, and with Harald Hardrada and William the Bastard both eying up the English throne the nobles in England would need a strong immediate successor they could rally round to battle those two threats, and Godwinson was a proven general, warrior and leader while also being the most powerful noble in the country so he fit the bill perfectly and was in an ideal position to enforce his claim to the throne.