Exporting a vehicle from UK to EU

Hello, I'm French, living in France, and I'd like to purchase a second-hand vehicle in the UK and export it to France. It is for personal use, so I guess that I just need to do a declaration by conduct or an oral declaration at the border. Is that correct? Are there specific documents I need? And then I will have to do the customs clearance in France? Do we have to inform the DVLA of the permanent export? Thank you

Hi Marie Sen.
Yes, for permanent export customer needs to inform DVLA about the vehicle.
For more information please check here:
Taking a vehicle out of the UK Skip to contents of guide Contents
Thank you.