I have heard of someone who took hatching eggs from England on the plane and managed to persuade customs at Heathrow NOT to send the box through the X-ray scanner, as that kills the eggs. I discussed it at East Midlands and they told me the only way the eggs would avoid the scanner is if I had all the correct documentation for exemption. If you fly from France that will be a problem- I've taken eating eggs many times but they all go through the machine in hand luggage. Your exemption paperwork would need to be translated officially into French. So if you want to try and ask them to avoid the scanner, that's a risky unofficial route even if your French is great.
No problem in a car though. Just put them in French egg boxes with your other supermarket shopping. I'd expect hatching rates to be better than those eggs which are posted in England and 'thrown' through the system. I am under the impression that egg trafficking is commonplace as I know of people with English breeds.
What breed are you trying to import? There is a facebook group here called 'Chicken Keepers in France' that may be able to help. You might be able to get some eggs from 'la Ferme de Beaumont' (
www.fermedebeaumont.com) which is a rare breed company based in Eu, a Northern town betweenDieppe and Abbeville. It's a difficult place to find, but I got there in the end- just two hours from Calais.