The method of laser spectroscopy in supersonic gas jets was proposed for high-resolution and high-efficiency in-gas laser ionization and spectroscopy studies of short-lived nuclei. The flow properties of such supersonic gas jets have been characterized under off-line conditions. Planar laser-induced fluorescence spectroscopy of seeded copper atoms has been applied to nonintrusively measure velocity, temperature, and relative density profiles of gas jets formed by different de Laval nozzles. For validation, planar laser-induced fluorescence spectroscopy was applied on supersonic free jets with well-known flow parameters. The performance of the in-gas-jet laser spectroscopy method is determined by the achievable spectral resolution, which requires an optimization and a precise manufacturing of the nozzle inner contour as well as a pressure matching of the background medium at the nozzle exit. Our studies now enable a thorough understanding and quantification of these requirements and a determination of the final performance of the in-gas-jet method. Additionally, a comparison between the experimental results and the numerical calculations was performed for the temperature, velocity, and Mach number profiles of underexpanded and quasiuniform jets formed by a de Laval nozzle.