Re: what "FOI is for": see my previous comment above excerpting from FREEDOM OF INFORMATION IN FRANCE, LAW AND PRACTICE

Re: a hypothetical LLM: French FOI law covers all document formats. The CADA and courts have routinely recognized that documents produced by the government in formats such as audio recordings, x-rays, photographs (of submerged shipwrecks, no less), application source code, and computer algorithms may be considered administrative documents, communicable to the public.

So, if the French government produced an LLM and front end then, yes, that LLM model and its front end would be an administrative document, in principle communicable to the public. To me that does not seem improper or difficult or strange to imagine.