When moving to France, as with any move, what to keep and what to throw out are very important. My personal suggestion to that you ship as much non-electoral furnishings as possible. Even with the added cost of shipping, furnishings bought in the states are cheaper than in France.
When we moved in the summer of 1002 - Boston to France our shipping costs were around $3,000, door to door, for about 100 cubic yards. That price was for anywhere in France. We shipped via boat and it took under two months for our furnishings to arrive. We shipped three futons with frames, a kitchen table, eight chairs and lots of others stuff, we had over forty boxes. Our things went through England and then came to France in a truck. We paid no taxes or duties, as everything we shipped was over six months old.
Furniture - As stated above ship as much as you can, within reason of course, what you might think about is that French housing is in general small than in the states, so large furnishings might not be worth it.
Appliances - This is up to you, in France the voltage is 220 and not 110 as in the states. This means that in order for American appliances to work in France you would need to get transformer. This is possible, I know of many Americans that have done this. We did not we just bought new in France. American appliances are big and France kitchens small so things like a refrigerator can be too big. Washing machines are not worth shipping; in France washing machines only have a cold-water intake as the machine itself heats the water. So to get an American washing machine to work in France you will need to do some plumbing.
Computers - Work fine in France all you have to do is change the switch in the back from 110 to 220. Also you will need to set your modem country configuration to France, as France uses a different tonality than the states.
Books - Not a bad idea to bring a lot over, as books here are more then in the states. Most major urban areas have English language bookstores.
Clothes - You will be surprised at how much the French dress like Americans, so don't think that you need to change your wardrobe to fit in. That along with the fact that clothes are more expensive in France means you should bring as much as you can.