For constructing a formal language we begin with an alphabet, now that we have the concept of alphabet we derive the concept of string, after we develop de concept of formula and finally the concept of well-formed formula. Now, the formal language can be seen as the set of all the well-formed formulas.
Once we have a formal language we can make an interpretation of the language, in other words, a model. But, what is the structure of a model of a formal language? In the sense that for a formal language we have alphabet-strings-formulas-(well-formed formulas), this would be the strucutre of a formal language in a sense of construction. That is my quistion bua about the model of a formal language. In the sense of construction, what is the structure of a model of a formal language?
Long comment
A Formal language, as you say, is a formal (i.e. mathematical) model (in the common sense term) of human language: alphabet, expressions (words), sentences (formulas).
We assume that all syntactically correct sentences (i.e. well-formed formulas) are meaningful.
How to give meaning to sentences?
Building an interpretation based on a domain of discourse, i.e. a collection of objects with their properties, like the natural numbers for the formal theory of arithmetic, usually called (Mathematical) structure.
We define rules to assign meaning to constant of the language: they will refer to fixed objects of the domain (the symbol $0$ will be the name for the number zero), and rules to "compute" the reference of terms (names) and with them the meaning (truth value) of sentences, using the rule for interpreting logical constants (e.g.connectives) that are fixed and do not change according to the interpretation.
When we use a formal language, like that of predicate calculus, to formalize a mathematical theory, like formal arithmetic, we assume some axioms, i.e. sentences in the formal language that express "basic facts" about the intended interpretation of the theory.
Example: formula $\forall x\ (0\neq S(x))$ expresses the fact that there is an "initial" element of the number sequence.
If all the axioms of the formal theory $T$ are true in a certain interpretation based on a structure $\mathcal M$, we say that the structure is a model for $T$: