Easy, they don't. The HADOPI authority harvests IPs from swarms, and the warnings are sent on the basis that your ip being there means you are a thief.
Of course, as an added bonus, you cannot argue with them, unless you have installed a gov. spyware to 'secure your connection'. Oh wait, you still can't argue with them, you have to take it to courts, after your internets have been cut off.
Actually, I'm not even sure you have any right to find out where or when your IP was sniffed.
I, for one, heartily welcome the latest addition to our Great French Police State.