Hi Melis,
I have left replying as I was hoping that someone in France would provide you with some help. My understanding is that since the UK left the European Union (i.e. Brexit) that the French authorities will not accept paperwork regarding a UK built kit car. Also as far as I am aware KVA never supplied complete cars, only parts to build a GT40 replica using parts from other cars, i.e Ford Cortina and Granada. Therefore no one will have what you describe as an 'Assembly Invoice'. There are people on this forum who probably have very old invoices from KVA for kit parts but I do not believe that will help you.
Having said the above, it is known that people in France have managed to find a way to register their car. Therefore I recommend that you ask around amongst clubs in France to try and get some help.
I hope our friends on this forum provide some help for you.
Best wishes
Steve