" if Ehresmann had the idea to compare on one hand (G,X)-structures and on the other hand manifolds or geometrical objects to be modeled on them"?
After a new look at the text, I believe that the answer to your question is "yes" to a large extent; this requires some precision. Ehresmann is interested in the "relations between Group Theory and Topology: between the global properties and the infinitesimal properties of a space" (p. 87). Of course, this paper was published in the same year as Whitney's definition of smooth manifolds by atlases (Whitney, Hassler (1936). "Differentiable Manifolds". Annals of Mathematics. Annals of Mathematics. 37 (3): 645–680. doi:10.2307/1968482. JSTOR 196848) Ehresmann has no such definition, but the objects he treats of are on the one hand topological manifolds, called by him "manifolds" (first lines of p. 88); and on the other hand (local) Lie groups defined in the (real) analytic category (p. 88). At the end of p. 89 and beginning of p. 90 he defines a homogeneous space (resp. a locally homogeneous space) as a manifold together with an action (resp. a local action) of a Lie group; and then he remarks that the manifold then becomes (real) analytic in the sense that it admits local coordinates such that the coordinate changes are analytic (p. 90). At the beginning of p. 91 he defines his program as "find all the locally homogeneous spaces which are locally isomorphic to a given (locally) homogeneous space". I'm not a specialist in the history of all these notions in that period; probably a study of the papers that he cites in the bibliography would allow one to understand which part of these ideas was actually original, which part was already known or at least "in the air".