My 2 cats flew the other way, from Paris to LA.
We gave them tranquilizers at the recommendation of the vet. They flew F on Lufthansa and where very well behaved.
I highly recommend giving your cat something to calm it, even if the vet doesn't recommend it. One of our cats is very sick and fragile and the vet told us to give him something.
Now they are very happy in LA, they enjoy a garden and someone with them all the time. They are thriving.