I've read several texts on the topic but I'm still not sure whether I got the concept right. Saussure says that language is a form, not substance. I understand that as saying that language is closer to a mathematical system (a natural law) than to a phenomenon (a thing created by the big bang). Could this be a correct interpretation?
Saussure is playing with two traditional dicotomies : the aristotelian : form/matter (their union is the substance) and the "(traditional) linguistic : form/content.
See CLG, Ch.4:
[ page 156 ] La langue comme pensée organisée dans la matière phonique.
The langue is a "structured" whole, that organizes the thought (pensée, idées) as well as the sound (matière phonique, sons).
[ page 157 ] On pourrait appeler la langue le domaine des articulations[...]: chaque terme linguistique est un petit membre, un articulus où une idée se fixe dans un son et où un son devient le signe d’une idée.
Thus, the langue is a relational structure that gives form both thought and sound.
[ page 158 ] La langue est encore comparable à une feuille de papier : la pensée est le recto et le son le verso ; [...] dans la langue, on ne saurait isoler ni le son de la pensée, ni la pensée du son ; on n’y arriverait que par une abstraction.
This means that is not correct to identify thought with content and sound with form.
Neither we can identify sound with matter organized by thougth, the form. The langue (the "relational structure") is the form that organizes both the signifier (the expression) and the signidied (the idea) :
[ page 158 ] La linguistique travaille donc sur le terrain limitrophe où les éléments des deux ordres se combinent ; cette combinaison produit une forme, non une substance.
The idea of language as form is often referred to as structural linguistics. As you said, it treats it like a mathematical or logical system whose content is secondary to the rules governing the relations between the words and other semantical units. Noam Chomsky describes it as follows:
"Structural linguistics has enormously broadened the scope of information available to us and has extended immeasurably the reliability of such data. It has shown that there are structural relations in language that can be studied abstractly. It has raised the precision of discourse about language to entirely new levels. But I think that its major contribution may prove to be one for which, paradoxically, it has been very severely criticized. I refer to the careful and serious attempt to construct 'discovery procedures,' those techniques of segmentation and classification to which Saussure referred. This attempt was a failure – I think that is now generally understood. It was a failure because such techniques are at best limited to the phenomena of surface structure and cannot, therefore, reveal the mechanisms that underlie the creative aspect of language use and the expression of semantic content." (Noam Chomsky, Language and Mind, pgs. 19-20)
Chomsky's criticism of Saussure on this point reflects the fact that Chomsky has developed a system to analyze what he refers to as the deep structure of language, and that the structuralism of Saussure is not able to demonstrate the underlying meaning that is present in language:
"He held that when all such analysis is complete, the structure of the language is, of necessity, completely revealed, and the science of linguistics will have realized its task completely. Evidently, such taxonomic analysis leaves no place for deep structure in the sense of philosophical grammar. For example, the system of three propositions underlying the sentence 'Invisible God created the visible world' cannot be derived from this sentence by segmentation and classification of segmented units, nor can the transformational operations relating the deep and surface structure, in this case, be expressed in terms of paradigmatic and syntagmatic structures." (Noam Chomsky, Language and Mind, pg. 17)
Chomsky gives an example to illustrate the difference between deep structure and surface structure with respect to the sentence "A wise man is honest":
The more complex diagram is, of course, the deep structure, and it can be seen that even simple sentences often have propositional ideas underlying them which are not explicitly expressed. The second diagram, which represents the structuralist approach of Saussure, only classifies words into a taxonomy.