If the "team" was a joint law enforcement task force based in the United States, the CIA officer could theoretically be given a Special Deputy U.S. Marshal badge, which would give them law enforcement officer privileges, but that ain't this show. And, honestly, I'm not sure what this show is yet, since we didn't really see the "team" working as a proper team.
But, the show seems to be about an espionage-y team that works outside the United States. That scenario is classic CIA territory and not at all FBI territory, especially as the FBI has no true law enforcement jurisdiction outside the United States. The FBI does work on investigations outside the States and liaison with foreign law enforcement agencies, primarily through legal attachés who are based in embassies (FBI.gov summary). Yet, this show makes it look like the FBI has a mini field office in the Paris embassy.
So, the whole FBI vs CIA thing doesn't really work for me. If they wanted to do antagonistic agencies where overlapping jurisdictions actually make sense, a joint team with the CIA and some other foreign intelligence service, say the U.K.'s Secret Intelligence Service (SIS or "MI6" in Hollywood jargon) would work much better, drama-wise. (And, on the business end of things, could perhaps open up the option of a joint production to spread out the financing and risk.) Also, an option for antagonistic inter-federal agencies would have been to make one of the leads work for the Defense Intelligence Agency (DIA), which is under the Department of Defense. Like the CIA, they have a Clandestine section.
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I guess the show is just going to overlook the fact that the NSA Guy kinda paid off a Russian mercenary to kill someone (the helicopter pilot).
They didn't give Ana Ortiz too much to do except confirm the identity of a CIA operative over an apparently unsecured phone line. And, how did she even have access to the file?
Speaking of bad OPSEC, the characters' codenames are based on their initials (Foley mentioned this in an interview).
Also, discussing your latest op in the public lobby of an Embassy is not a good idea.