Yes, I moved my cat and dog over via Paris this past October. My cat is a snubnose (half persian), so I really had no other choice but to have her in the cabin with me as a lot of airlines will not take a snubnose cat/dog in the hold because of the possibility of breathing problems.
I flew with Delta/AirFrance, so it was the cost of my flight, plus $200. each for each pet, so it was a huge savings from going into Heathrow with both animals.
I got the cat a really good, sturdy carrier about 6 weeks prior to our departure, I lured her in with catnip, fed her in there every day and once or twice a week I would zip her up inside overnight so she would be used to staying in there for a long period of time. I also got a TSA approved harness and leash for going through security and when we arrived at Calais and she had to be removed from her carrier. The harness, leash, collapsible water/food dishes and pads for the carrier were all bought from a company called Dryfur, get on their site and do some reading, it will help put your mind to rest!
As far as traveling with her, she was fine, she got a little antsy on the take off and landing on the first leg of our journey as that was a small commuter plane, but on the Paris leg, she slept the whole night through. We arrived in Paris, no one blinked an eye, no one looked at paperwork for either animal in Paris. DH picked us all up, we drove to Calais, zipped through the UK Animal Reception, drove onto the train for the Eurotunnel and back home.
Both the cat and dog handled the journey very nicely and they are both curled up next to me right now!
If you have any questions about going to Paris with the cat, PM if you want