Considering this would have been the equivalent to a modern someone working under a CEO declaring himself CEO of a different company AND taking all the resources that had been assigned to him by his old CEO along with him, how was this handled by the reigning French monarch? Did he try to to denounce it as breaking some sort of oath or contract between a vassal and his lord? Was it considered scandalous by the other French vassals? Were there other monarchs like the Holy Roman Emperor who spoke out against it on the basis of it forming a bad precedent, e.g. wouldn't want the King of Bohemia to suddenly declare himself the Bohemian Emperor and independent of the HRE. What, if any role did the Pope play in how all this played out?
You must understand that William did not just decide to conquer England on a whim. He had a claim to the English throne that appeared far more legitimate than that of Harold Godwinson. William had appealed to the Pope for support in his pursuit of what he considered rightfully his and did indeed receive Papal support, signified by a Papal banner to carry into battle. The combination of Papal support and the apparent strength of William’s claim would have satisfied most European rulers that he was simply claiming what was his.
As for the King of France, he had always had it in for the Dukes of Normandy. They were essentially a renegade vassal and had been for some years before 1066. He had tried multiple times to bring them to heel and had failed. Philip was constantly looking for ways to weaken Williams position in Normandy, which often involved secretly or overtly backing a rebellion against William in Normandy. Essentially the state of relations between France and Normandy was pretty much the same as between France and England later. Technically a vassal in regards to Normandy and later Aquitaine, but in reality completely beyond the control of the French king.