The adjective technique doesn't necessarily mean matérielle. It is essentially the opposite of non-technique.
I.- D. − [Par opposition à général, commun, courant] Qui relève d'une activité ou d'une discipline spécialisée, et suppose des connaissances spécifiques. Dictionnaire, ouvrage, revue technique; discussion technique. La presse technique. Il y a tout de même des gens qui ont misé toute leur passion sur une technique et pour qui s'édite une presse technique fort abondante (Civilis. écr., 1939, p. 36-13). Ces cours s'adressent à des auditeurs qui possèdent une solide culture générale et technique (Encyclop. éduc., 1960, p. 178).
In the MWD, the second definition of "Nontechnical" is:
b: not being or using technical or specialized terminology.
// The doctor explained the effects of the disease in nontechnical terms.
// Most of the writing in this book is nontechnical, meaning that it can be understood by the 99.7 percent of the public who are trained in neither science nor engineering.
The opposite of "nontechnical" would then be: "something that might not be easily understood by someone who does not have a science or engineering background".
That's close to what a document d'architecture technique can be. It describes what is "under the hood", how things are done (whether hardware or not). On the opposite, the document d'architecture fonctionnelle describes the high level functions of the system, i.e. what the end-users expect described in a way that does not require scientific or technical expertise1. We also call these documents the documentation métier, meaning targeted to the user, not the builder. Two different layers of competencies are addressed.
The architecture technique often encompasses the architecture matérielle but is not limited to it and might even not include anything material (a piece of software has a technical architecture too, security is immaterial but still part of the architecture technique).
I don't see any fundamental difference between the French expression document d'architecture technique and what can be referred to as technical documentation in English or arquitectura técnica in Spanish. However, I agree technique is not used the same way as matérielle or fonctionnelle. Technique applies to document d'architecture as a whole while matérielle and fonctionnelle only apply to architecture. We can say, c'est un document technique but not c'est un document fonctionnel or c'est un document matériel. Nevertheless, architecture technique might be used alone.
"Technical" and "functional" are used to qualify "architecture" in this wikipedia page the same way their word by word translations in French would be:
In the case of a so-called technical architecture, the architecture must be communicated to software developers; a functional architecture is communicated to various stakeholders and users.
You wrote: In addition, ALL documents describing a system need to be technical, that is, should be the application of theoretical knowledge in the concerned domain (e.g. l'Architecture Fonctionnelle is necessary a technical document which refers to the functional description of the system).
You are right but the difference is the that the architecture fonctionnelle target readers will necessarily understand these documents because they use the vocabulary of their métier. On the opposite, a developer might be confortable with the architecture technique but have no clue about what functionalities the overall system will provide to the end users.
1 Of course, there are cases where the end user has a scientific and technical expertise anyway but that would generally be in a different domain.