One caveat on moving "all your stuff" over - houses and homes in general in France are considerably smaller than in the US. It can be difficult (and very frustrating) to try and find a place to live that will take an entire household full of US furniture and other "stuff."
Before moving everything over, do a thorough weeding out of large pieces or appliances and the like that won't be usable in France. You can sell off or store the bits you decide not to ship, but it makes little sense to ship them over, store them in France and then ship them back later. (It's difficult to get rid of large, American furniture and appliances over here.)
Best examples: US fridge freezers are just too large for most French kitchens, although you're starting to see a few "US style" refrigerators here in the stores. And just search the forum here for several discussions about US vs. European washers and dryers. (European washing machines generally connect only to the cold water outlet because they heat their own water in the machine.)
Furniture is much the same. I've heard that IKEA had to redesign much of their furniture for their US stores because it was "too small" for the US market.
Cheers,
Bev