When I was in Paris, it happened to me ten times or more. Walking on a public place, a man or a woman would pop out of nowhere, golden ring in hand, and say "hey, mister, is this yours?"
It's a well known scam. You get to keep the ring, and the ring bearer will ask you for some compensation. It will turn out the ring is worthless, so you will be out a couple of euros or so.
It's interesting in some ways, though.
It relies on the victim being dishonest, since the ring is not theirs.
The amount of money gained by the scammer is at the victim's discretion.
If you don't give the scammer anything, he will, at most, yell at you for being a cheap bastard, and it's done in very public places, so the danger of violence is negligible.
Since the victim is also doing something morally reprehensive, and lying, the risk of the scammer being charged with anything is negligible.
It's almost like some sort of weird sale:
"Here's something of no value that looks valuable! Is it yours? (I know it isn't)" "I will bet on it being valuable and pretend it's mine!" "So, how much is appeasing your remorse about scamming me out of a probably worthless ring worth?" "I'd say 3 euros, my good man!" "Deal!"
How can it be worth their while to do this? I would guess their success rate at perhaps 5% and they probably don't make more than 5 euros on a successful transaction
All in all, it seems fairly harmless, just annoying, and french people have actually chased me down the street to return me something I forgot in a bar. Then again, I also was peed on a foot by a badly burn-disfigured guy in a wheelchair, on Champs Elysees, so YMMV.