You will need your official Dichiarazione di Vendita (Declaration of Sale) giving details of who the parties involved were (for instance, a dealer or previous owner) and the sale price signed by a notary. That is because no other form of receipt or proof of ownership constitutes legal ownership in Italy. Before leaving Italy with your car you will need proof of valid insurance to drive it out of Italy and for the first few days in France. So first you contact your insurance broker here and ask him/her to fax you the Certificate of Insurance immediately. You may not be able to insure the car through the Italian registration number but you can quote the chassis number and this is acceptable for the journey back to France. Some Italian insurance companies might offer two to five days insurance cover at a reasonable price which would be an alternative that would allow you to get to your insurance agent here. Assuming your car still has valid road tax, it will obviously carry Italian number plates. Number plates in Italy are issued by the local authorities and those must be returned to the Comune (Council) as proof that the car is no longer in use on the road in Italy. For re-registration you will need the original registration document, the LIbretto, the Dichiarazione di Vendita that was signed and stamped by the notary. If you have it, you will need at least a photocopy of a document that gives all the details of the car's official type approval, the Foglio di immatricolazione. Finally, you may well need the official document called the the Certificato di Proprieta, that states that the car has been 'demolished' which is how it is classified as being taken of the Italian roads for export . The catch with that last one is that you would be expected to surrender your plates and would be without until you get your carte gris here from the préfecture.
My wife is a native Italian speaker (Swiss not Italian) and helped a neighbour do this in England who was born in Italy but grew up and has always lived in England and whose Italian was not up to doing this. However, within the EU each country ‘knows’ each others’ registration and deregistration procedures and it appears we are normally obliged to go through the complete process at both ends. Lots of UK cars come, are sold and eventually scrapped here because there is seldom any attention paid to formal deregistration as a rule, although we apparently should so that the numbers can be cancelled. Forget that, there is no comparison. With Italy it is different because it is absolutely demanded and the French will probably say nothing if you do not have all documents. However, try to register here and then notify the Italian Comune where the car is registered once all the palaver here is done. As our friend in England, they may allow you to ‘destroy’ your registration plates yourself. If the car remains on the road and you ever have a serious accident there is apparently a chance that the chassis number that the Italians know will show that your car has been classed as missing and then you will have a bureaucratic nightmare on your hands.
And some people think French bureaucracy is bad. That is one of the reasons we chose never to live in Italy.