Article L211-23 of the Code rural et de la pêche maritime defines strays.

For a dog the definition is pretty much common sense, roughly translated, if it's out of earshot of the person responsible for it, no longer under their effective supervision or more than one hundred metres away from them, then it's a stray. Seems reasonable to me.

For a cat the definition raises some practical difficulties. Any cat that is not identified found more than 200 metres from habitation or more than 1000m from it's owner's home and not under their supervision as well as any cat who's owner is not known  found on the public highway or anyone else's property is a stray.

As the code rural acknowledges, and cat owners know, cats like to wander. Whilst away they may visit someone else's home for some attention or a bite to eat. If they do that often enough and they are not visibly identified than there is a risk that they will be taken for a stray.  

What should you do if you find a cat that's not identified and without an obvious owner or if one comes visiting. How can you tell if it's a stray? I believe that difficulty is responsible for a lot of misery to owners and unnecessary work for animal protection associations.

If you think that the cat is a stray and take it to the town hall, then if it isn't identified it should end up in the town kennels where its fate is uncertain.  However there is a chance that it will be reunited with its owners if they actively search for it. If not then it may be given to an animal protection association for adoption or, in the worse case,  put down.

If you don't think that its a stray and leave it to its own devices, it may wander back to its home and live happily every after or it may be a stray and you might be leaving it to suffer in the wild. What should you do?

There are no hard and fast rules. If you find a cat in the middle of nowhere and its very friendly or its very young then it may well have been abandoned.  

Evaluate a suspected stray's condition: if it looks clean and the pads of its paws are not worn then it's probably not a stray...  unless it's just been abandoned! If its condition is bad and/or deteriorates then it's more likely to be a stray.

We have had some success with asking people to put a (safety) collar on the suspected stray with a message saying, “Please get this cat identified as it is suspected of being a stray/ Veuillez faire identifier ce chat parce qu'on soupconne qu'il est en divagation.” There is a risk that by leaving a cat to its own devices it has an accident, but if you take it in or take it to the town hall you might be causing a problem for its owner.

It's quite a big responsibility because the stakes are so high: get it wrong and you may have taken someone's animal or you've failed to help an animal in need. The worse thing is that you only find out if you've made the right decision if you reunite the animal with its owner. In all the other cases, you either discover that you've made a mistake and something bad happens or you never find out for good or for bad which makes it difficult to refine your technique. And this only happens because people don't identify their animal. So for your own peace of mind (and to make our work a bit easier) please ensure that it's possible to tell that your animals belong to someone.