You need to have some idea of weight and cube. A 40 foot container port to port France / US can cost around 4,000 $. Then there's packing and other ancillary charges. Depends where in the US, and in France, to calculate the extra freight rate. (To give you an idea of the space available, a 20' container is approx 33m3, a 40' container 67m3). But in practice you fit at best 5m3 less in each, even with a load of nothing but cartons that are easy to stack inside.
If you ask a number of companies for quotes to ship a container load of personal effects, 20' or 40', you'll get a rough idea of the going rate. Where did the figure of 25-40,000 $ come from?