Moving to France with your personal effects and furniture can be done without paying an import tax, as long as the property has been owned and used for six months or more, and is intended for personal use. 

If you are considering packing up all your belongings and moving it overseas, contact a "container" shipper with international experience.  You will be billed on "volume" and not weight this way.  It makes moving your belongings less stressful and means you can bring more! 

French law gives you one year in which to ship the items to your new French residence upon receiving the “Change of Residence Certification” from French customs or the French consulate in your area. This must be stamped by a French consular official. 

An itemized list of all the contents of the shipment must be prepared in duplicate, indicating the value of each piece, in your native currency. 

Household goods and personal effects imported free of duty and tax as part of your moving to France may not be sold or otherwise disposed of for a period of 1 year after they have been cleared through customs, unless duties and taxes are paid at the applicable rate. Duties and taxes must be paid before the sale is completed.

When considering what to move with you to France, remember that there are lovely home furnishings available in France.  This may be the time that you "downsize" and consider bringing only the items that hold sentimental value.  You can always pack your items securely in boxes, store them, and retrieve them in the future.  An empty shelf only means more room to create new memories!