Hello,
Disclaimer: this experience is 5 years old and applies to LHR only.
When we moved here 5 years ago with our 4 Australian Shepherds, they had to fly cargo.
And as there was a requirement that shippers of cargo needed to be "known shippers", we had to hire a pet transport company. (I think this requirement came in shortly after the printer ink cartridge bombs were found.)
The dogs managed fine and were well treated as far as we could tell.
Coming in from the US, there is no quarantine requirement provided all the paperwork was correct.
We flew nonstop, Newark to LHR on UA.
As the dogs were used to being indoors most of the night without relief, we chose a night flight.
That way, upon arrival in LHR and transported to the Animal Arrival Center, they were ok when they were let out into the kennel.
The pet transport company was excellent. They handled all the paperwork on the US side and on the UK side. All we had to do was to hand the crates to the staff at EWR and pick up the dogs on the other side.
That said, a few cautions to get to that point:
Make sure you study and follow the rules/regulations closely, including the required minimum size for crates and all the vet paperwork that is needed. We needed to get the dogs chipped a second time because their previous chip was US-centric and we were not sure the EU chip readers would read them (why take the chance?) Also, we had to redo one of the vet examinations because the dog had been re-chipped AFTER the initial pet passport exam. The chipping has to be done first so the vet can certify that the dog with a certain chip number is the one that was examined.
Also, do not tranquillise the dog. You want it to have its wits in the very slight case something does happen.
But part of what you will be paying the pet transport company is for their knowledge of what the paperwork needs to be so there are no surprises on arrival. Map out the timelines, schedule the trip and run it by the transport company. And book early as UA only took a certain number of live animals on each trip.
I would suggest you look at whether it is really worth the effort and cost. For example, if the pet passport is not filled out correctly on arrival at UK passport control at the ferry dock, they can require the animal to be placed into quarantine until you take the animal back to France and have a French vet resolve any deficiencies.
Again, I cannot speak of how CDG will handle things. Your mileage will likely be different.