We report on the spectroscopy in a resonant vapor film, in a regime in which the inhomogeneous transit time induces a velocity selection. For cell thickness (10--1000 \ensuremath{\mu}m) smaller than the transverse dimensions and for low enough atomic density, the atomic trajectories are essentially free flights from wall to wall. Hence, a single laser beam irradiation is sufficient to observe sub-Doppler resonances because of the transient atomic response, which enhances the response of the slowest atoms flying nearly parallel to the wall. The peculiar features of this velocity selection are presented in the linear regime as well as in the case of saturation induced by the optical pumping. Also, we report, in the case of the Cs
D2 line (852 nm), on the passage from a two-level linear-response regime to an optical pumping regime when increasing the incident intensity. We also describe the influence of several other parameters, including cell thickness and laser beam size and shape, on the experimental line shapes. An extension to Doppler-free polarization spectroscopy in a thin cell with a single beam, and to saturated absorption, is also reported.