Police Crime Reference Number

11:57 Jul 4, 2015 

@Daryo

How "reporting a crime to the UK police works" has no relevance to Asker's question (assuming it works any differently in other law-governed countries - please see the Belgian reference below); and what is needed here is a term that makes sense to a French audience.
Still, Asker has the option to mention the original English term (in brackets, for example), as suggested by Tony.

14:23 Jul 3, 2015 

Note that the systems used by the police forces in the different countries are not exactly the same, and so a direct translation of this will not be very helpful, save by way of an explanation. If what you are doing is a localization, then you probably ought to leave the original EN term, and then add an explanation to the effect of (or the local equivalent in your country).

Note that in France there may also be a difference in procedures or documentation between the Gendarmerie Nationale and the Police Judiciaire, just to complicate matters.

In particular, I am far from sure that it would be referred to as a 'crime' before it has gone to Court and been confirmed as such; I think it will be regarded as a 'complaint' until such time as an actual 'crime' is proven.