You may want to talk to an international mover to get a closer estimate of the costs. There's also insurance for your shipment (which is normally a % on the value of the shipment as declared).
You'll need to have a detailed listing of the contents (with approximate dates of acquisition and current market value of the goods) in order to clear customs when your stuff arrives in France. As long as you're coming over on a long-stay visa, your household goods can enter France duty free and without VAT - but for items you've owned for less than six months, you'll be charged VAT on import (at 19.6%). Most international movers will have a customs agent who can handle the clearance for you.
And then there's the cost of hauling your container from wherever it arrives to your new home. If you work with a mover, they'll use their correspondent in the area (usually another moving company).
Many of the big moving companies in the US (Atlas, United, Allied, Bekins, etc.) have international capabilities and should be able to give you estimates regarding the costs of such a move.
Cheers,
Bev