I suspect the reason that the police checked the surrounding streets was precisely because they knew that quite a high percentage of 'stolen' cars (both in the UK and in France) have simply been 'mislaid'.
I once left the local bowls club (where I ran the bar) to return to my car , which I knew that I'd parked alongside the clubhouse, only to find it missing. Knowing what an idiot I can be when it comes to such matters, I carefully ran through the events of the evening. Yes, I remembered driving from home to the clubhouse (rather than walking, as I'd usually do) because the car was full of stock from the cash-&-carry. Yes, I remembered several trips, to and from the car, carrying that stock into the clubhouse, and I was absolutely certain that my car had been immediately outside the clubhouse at the time. It wasn't there now, so it must have been stolen. I was fumbling in the dark for my mobile phone, to call the police, when I noticed that a car was still parked in the darkness at the very far side of the car park. When I got to it, I discovered it was mine, so I drove it home, still totally mystified as to how it could have moved from one side of the car park to the other. It wasn't until the following day that I remembered that I'd gone home half way through the evening to get some more change and, upon finding the car park almost full, parked on the very edge of it ;-)