I wrote about Arthur Fremantle a few months ago, here: https://www.reddit.com/r/AskHistorians/comments/7hhlis/where_there_any_travel_restrictions_put_on/

Fremantle was an unofficial observer from England, but was not a sanctioned or official "monitor" as OP suggests, however. Fremantle came on his own to just sort of sightsee, but had the amazing good fortune getting in with some prominent company, north and south. Come to think of it, I'm not immediately aware of any official observers sent by France or England to "examine the course of the war."

OP - can you cite a source for this claim, or provide any background on this? I'd be interested to read more about official "monitors."

In the temporary absence of a specific answer, /u/vonadler did an answer a month or so ago about whether the Civil War impacted European military practice. Obviously, this won't be centred on the immediate perceptions, which is what you have asked for, but it'll be a start. Also pinging in /u/dandan_noodles just in case.