I am not sure if your question points at how i personaly would handle it ruleswise or how i judge the situation - so one after the other!
Bear with me, i know as much about gallia as a toddler about quantum mechanics ( also, the faction status pages are a bit outdated it seems?!)
Sot he Situation is that the CR cooperates with the Council to fight against the GRN as well as working with the Corse for an unspecified goal within Gallia.
So i take it that "in reality" the Council and the Union Corse are no longer friendly to each other and the Council has a good reason to dislike the CR-UC cooperation.
Now...can the Council know of the CR working on both sides?
-Yes, if the UC operate in areas where the CR-GRN combat takes place- they would have a solid chance of witnessing the CR-C tag team.
-Yes, if the GRN ever discusses anything about getting in and out of Gallia or recent battles officially or randomly with some of the UC - at least the GRN faction status hints that this is plausible.
- Yes if there is any kind of news coverage or war reporters reporting on what happens on the fontlines( Which i would strongly suggest)
Now can the Council know of the CR in Gallia? I take it that at least in theory there are ways to not bump into the GRN on your way in...so it leaves the question of what do the CR do in Gallia?
- Behind the frontline assault? Then they are busted, see news coverage.
- Smuggling? Depends where to...if only to Union Corse bases, i would say it can stay undetected(probably not forever) - if somewhere else...then someone will notice and the CR are busted.
So to sum it up- if the CR is extremely extremely careful, they might have a chance of going undetected. If they get caught there may or may not be consequences - i have little knowledge of the operative procedures of the Council and their morality/buyability...so you might better know what happens to people who betray them.
My gut feeling tells me that i would simply cross the CR-C alliance and drop it to a neutral point. The Council doesn't like them in Gallia and being snake tongued and the CR seems to have some kind of reason to go to Gallias heartland that is worthy to risk the wrath of the Council. I have no clue about the councils military strength- but for the CR i remember them as rather bloody nosed and down in the dirt- which means that they might not be such a big addition tho the Councils interests in any way, making them even more droppable if they don't comply to their demands and lessening the reason to help out.
Neutral attitude suits well- other than that you could argue for the OC and the Brets to enter a formal Alliance ( just don't tell the Libertonians!)
And rulewise, this looks fine to me for a "grey" slot - if only temporary