I would place the ring in a tie or scarf holder that has a couple of ties/scarves and a single tie clip/brooch inside a cabin bag with a non-TSA lock on the bag that has just clothes otherwise. I would have the ring inside two ziploc bags so it can be easily located if dropped and include my contact info on it. [According to police, some homeless guy found my relative's very expensive wedding ring that she lost when coming out of a taxi. The homeless guy turned it in to a police precinct office and she was never able to find out who turned it in and reward him for his caring act. She probably would have gotten it back sooner from the homeless fellow if she had some contact info with the ring.]
On board the plane just before descent, taking out the ring and placing it in a zippered pocket of a pant you are wearing on arrival would almost certainly go unnoticed at CDG even were you to walk the red channel.
When I have precious luggage, I take car service from a major car service company and keep the precious items on my person or in my bag in the passenger compartment. For personal precious items, the hotel safe is better than a room safe. Either way, get it insured prior to travel if its loss would be material by your standards. And don't carry it around 24/7 in Paris or anywhere else for that matter. Things get lost more frequently than they get stolen, but transporting it on person around Paris will just increase the risks of both such unfortunate outcomes.