The dry etching reaction of solid copper surfaces with fluorine atoms or molecules has been studied with laser-induced fluorescence spectroscopy. The reaction product, copper monofluoride, CuF, is produced in the X(1) Sigma(+) electronic ground state and desorbs into the gas phase at surface temperatures above approximately 750 K. Rotationally resolved LIF excitation spectra of the (CII)-I-1 <-- X(1) Sigma(+) band system of CuF molecules desorbing from an isotopically purified (CU)-C-63 polycrystalline sample are obtained under conditions of coherent saturation. From the product state analysis it is deduced that the rovibrational product populations are in thermal equilibrium with the surface. The same holds for the translational velocity distribution obtained by Doppler-shift measurements. A pronounced polarization effect, particularly strong for Q branch transitions, can be traced back to photoselection of single-parity levels in the Lambda doublets of the (CII)-I-1 state. A theoretical analysis for the distribution of J vectors, based on the formalism of Greene and Zare, shows that the measured degree of polarization is quantitatively in agreement with an isotropic distribution of rotational angular momentum vectors. The vibrational and translational product equilibration is not affected by changing the reactants from F-2 molecules to F atoms, which increases the exoergicity of the overall reaction. The results are interpreted in terms of the absence of a barrier for desorption and a long residence time of the chemisorbed CuF molecules at the copper surface. The lack of any translational and rotational cooling is discussed within the framework of a model.