That's quite a fascinating connection with that idea of the Committee of Public Safety. In France, it was under the name Comité De Salut Public, which doesn't have the "C.O.P" abbreviation you're finding. But, if you find the connection useful for an exam that's great. If you find a historical document that makes the connection between the Comité and "cops" that could very usefully add to what I'm writing below. But, I don't know of any explicit source related to the Comiteé origin that your question suggests. All that to say, keep making those connections and follow the evidence to see if your hunches bear out.

Ultimately, "cop" has its basis before the French Revolution in several root-words across Europe. The Etymology Online Dictionary is useful in this regard, but "Cop" was attached to an extant and pre-French Revolution verb already in use in northern England:

The Online Etymology Dictionary says the verb "to cop" meant: "to seize, to catch, capture or arrest as a prisoner," and it is attested at its earliest at 1704 from a "northern British dialect." Its origins are uncertain, and they suggest it maybe came from the French caper , which meant "to seize, to take," which itself is from the Latin capere "to take." This is where we get our modern "caper" stories, usually involving the cops-and-robbers dynamics with stories like Sherlock Holmes, Columbo, Law and Order, etc.

Here we see an association with the verb "to cop" and the act of abduction, grabbing, taking, halting, etc. which if you're thinking in terms of the police, kind of makes sense. They're on the prowl to 'abduct' in a way robbers, thieves, murderers, etc.

But, the verb "to cop" may have also come from the Dutch kapen "to take," or from the Old Frisian word capia, which meant "to buy," which is related to the Old English word ceapian which became the word we use today as "cheap." We see in English today the phrase "cop out" or someone "copped out." It means sold and usually in the act of selling to cheapen the thing or to quite because of cowardice.

This second definition also kind of comes up. Calling someone a "copper" and then a "cop" might also suggest that the person who is a policeman "sold themselves out" in a way, that they've gone with the cowardly option to serve a state or security force that certain groups might see as oppressive. For example, an Irish union organizer in Chicago might see an Irish policeman as having sold out their people to serve the folks that are underpaying him or forcing him to work in unsafe working conditions. So, this hypothetical Irish officer has "sold out" or "copped" his Irish brethren to serve a robber baron.

And, even aside from the origin, to call someone a "cop" is usually shouted in opposition to a police officer's presence or action. Even if someone isn't explicitly calling them an "abductor" or a "sellout" or a "coward," as the origins of the term "cop" and its noun "copper" might imply, the negative connotation remains and may be the source of policefolks' dislike of the term, too.

​

Edit: cleared up some phrasing.