I can only contribute a small tidbit here. But the Pope officially supported William's claim to the throne after William sent an envoy with a trusted prior of his, Lanfranc (who later became the Archbishop of Canterbury). Lanfranc returned to William with a papal banner, which William brought with him when he invaded England.

I'm not sure about other monarchs at the time, besides Harold Hardrada who obviously tried to claim England for himself. But the French King, Philip, constantly tried to undermine William and allied himself with counts and lords who also opposed William in the decade or two following his conquering of England.

It's also important to note that European monarchs in the 11th century had much less power than those a century or so later. They had much less land and wealth. Take "France" for instance. France had numerous dukedoms with lords/rulers who were semi-loyal to the French "king," but by and large had a significant amount of autonomy, as demonstrated by William skirmishing with the French king numerous times. Therefore, I'm not sure if you could apply the term "monarch" to any of the kings of Western Europe during this time.