Once living here you have 3 months in which to register you car and obtain a French log book (carte grise).
I have just been through the process of registering our car in France myself and I have made a list of requirements/ procedures.
All requirements may not apply to your car; this can depend on the region you are living in and also the age/ model of your car.

You can get a list of actual documents required from your local Prefecture or Sous-Prefecture when you make your application for your Carte Grise (log book).

The first thing you will want to do is to fill out the export section of your UK registration certificate and send it back to the DVLA.

Second thing to do is to get your head lamps changed at a garage.
They need to be changed to French lights for obvious reason that they point the wrong way. This seems to be mandatory and not optional as I first thought.

Thirdly you need to get yourself a French MOT. (Controle techinque)
If you take your car in and you have not had the headlamps changed, they will automatically fail the MOT on that point alone.
Unlike in the UK this only needs to be performed every 2 years after the initial test.

Fourthly a proof of purchase (sales receipt) if you have one, with proof that VAT was paid in the country of origin (unless you bought it second-hand)

Next a Demande de certificat d'immatriculation d'un v'hicle (registration form) which can be obtained from your local Prefecture or sous-prefecture. You can also print this online from the government website from a link on our site and click on form CERFA 10672*03.

Next, go down to your local Prefecture or Sous-Prefecture with your registration form, (if you already have it) your original registration documents and your controle technique. You will need photocopies of these as well. Once there they will tell you what if any other documents are required.

This may include

An attestation de conformit? which in English is a certificate of conformity. If you bought your car at a garage this can be obtained through them or alternatively from the manufacturer. I am told that the need for this document varies depending on the age of you vehicle.

A certificat de r'gularit? fiscale, this can be obtained from the local h'tel d'impots. This is a customs certificate.
There should not be any customs duty or VAT payable if you bought the car second-hand or can provide a VAT invoice.

You will need to make a photocopy of each of your documents and take them along with the registration form as before to your local prefecture or sous-prefecture.

An administration fee will be payable, our car cost us 67, 38? at the time of registration in September 06.