I think Interpol can be used as a back-channel communication link between governments.
I think police organizations, while taking on a security role, will still have some concern over 'normal' crime.
It says Interpol's "work focuses primarily on public safety and battling terrorism, crimes against humanity, environmental crime, genocide, war crimes, organized crime, piracy, illicit traffic in works of art, illicit drug production, drug trafficking, weapons smuggling, human trafficking, money laundering, child pornography, white-collar crime, computer crime, intellectual property crime and corruption."
Even taking out genocide, war crimes, corruption, and terrorism all (of which may be war-related), there's still actually a fair amount of possible international crime to cooperate about.
Various crimes may have war-related concerns for a given nation, heightening their interest in handling a type of crime. For example,
smuggling as the smugglers may be considered damaging the war effort by pilfering national stores (weapons, medical equipment), aiding deserters, helping to transport spies, etc
So, where relations between France and the NATO governments (W Germany, England, Canada, USA, Netherlands, Denmark, Norway) may be cold, their police may still be willing to talk and share data, and cooperate (stopping crime is stopping crime) on some matters. Similarly, there is no reason for France and Italy or Greece (or the Soviet Union, however limited that cooperation was before the outbreak of the Twilight War) to avoid cooperating on matters related to crime. In both cases, there are personnel who have the personal relationships of cooperation (contacts) that they may use to keep in business.
Actually, it would be in keeping (IMHO) with French attitudes to try to keep Interpol running outside the war zones as an example of French International leadership.
Admittedly, a war zone is a difficult place to pursue criminals or criminal investigations but still...
Winter 2000, Madgeburg, Germany.
Bristol Myers, Leftenant with the 1st Wilts, is called in by his CO, and told to cooperate with a civilian, introduced as Jean Bertrand, Inspecteur Principal de la Surete Nationale de la France (you hear each nasally accented capital letter). Bertrand displays an official-looking badge and ID.
He explains at some length with painstaking detail in heavily accented English that he has tracked a criminal named Hugo Victoire, a French national, using various methods of intercepted communication, reconnaissance, physical evidence gathering, interrogation, to Magdeburg, where he is hiding, having been operating a white slavery ring, inducing German and Polish refugee women and even children (de touts les sex) into the industrie sexuelle in Marseille, some being sold on to North African, South American, and Middle Eastern countries. M. Bertrand appears quite worked up by the end of his lecture.
M. Bertrand wishes to take him in custody back to France to stand trial for his crimes (pronounced creem).
In response to the obvious question, the Old Man tells you this is
not a joke, that you and your squad
will accompany M. Bertrand about the town and help him locate this Hugo if possible. He will remind you that your file mentions you have a near fluency in French. Inspecteur Bertrand brought some supplies, including some 200 liters of petrol, 20 of which the leftenant can use to drive l'Inspecteur around town during his investigation and pursuit, and another 200 of which will be made available to the battalion upon the successful apprehension of Victoire...
T2K meets
The Third Man. Possibily culminating in an exciting chase through the town sewers if you wish

.
Another fun possibility, of course, is that Bertrand in a fake, another criminal going after a rival, Victoire, using the poor communications of the War Zone to keep his cover story...
I picked (on) a Frenchmen, but it could be a policeman of almost any nationality not involved in the immediate region's hostilities.
"...
charging a man with murder in this place was like handing out speeding tickets in the Indy 500." - Capt. Benjamin Willard,
Apocalypse Now
Uncle Ted