An original diffraction model for the analysis of grazing-incidence small-angle X-ray scattering (GISAXS) from the nanoparticle Langmuir films was developed. This model relies on the concept of the 2D hexagonal paracrystal and employs the distorted-wave Born approximation that is relevant for GISAXS measurements at the air/water interface when the angle of incidence is close to the critical value. The model comprises the cases of the close-packed nanoparticle monolayer and bilayer with the AB-type layer stacking. In this way, both the lateral (along the interface) and vertical (normal to the interface) correlations of the nanoparticle positions can be analyzed. The model was applied to an in situ GISAXS study of the formation of a silver nanoparticle Langmuir film during compression at the air/water interface in the Langmuir-Blodgett trough. Spherical nanoparticles of 5.8 +/- 0.6 nm diameter were employed. Different compression stages starting from the submonolayer up to the monolayer collapse via bilayer formation were analyzed in terms of the mean lateral interparticle distance, degree of paracrystal disorder, interlayer distance, vertical disorder, and layer-stacking type in the bilayer as well as the ratio between the monolayer and bilayer coverage in the final film. The model developed is applicable to any nanoparticle Langmuir film formed at the air/liquid interface to extract structural parameters on the nanoscale. The particular results obtained have direct implications on the preparation of silver plasmonic templates with "hot spots" for surface-enhanced Raman scattering.