It seems that in context of French grammar (at least in traditional grammar) talking about stative and dynamic verbs is not relevant. because there is no real progressive aspect in french and there is a tense like imperfect which we can use it for permanent or progressive situations for both stative and dynamic verbs. so syntactically it is not necessary to talk about stative and dynamic verbs in practice.
so syntax and morphology of French is not much sensetive to stative and dynamic verbs. and traditional grammar is actually syntax and morphology.
I am not expert in French grammar. Do you know any cases in French grammar which for explanation of syntactical or morphological behaviors something was said about the concept of stative and dynamic verbs?