We consider a lattice gas of particles that carry a two-component classical spin (i.e., a two-component unit vector). The pair interaction, restricted to nearest neighbors, implicitly includes hard-core repulsion, since each site can host one particle at most, and also contains ferromagnetic interaction between spins as well as nonmagnetic attraction between particles. We study thermodynamic properties and phase diagrams of the model by means of mean-field and two-site cluster approximations, and also by grand-canonical Monte Carlo simulations carried out for one value of the chemical potential; these aim at a quantitative check of the named approximations, as well as a more detailed description. Both mean-field and two-site cluster approximations were found to provide a qualitatively correct description for the thermodynamics of the model with nearest-neighbor interactions, and the predictions of the two-site cluster approximation were in satisfactory quantitative agreement with simulation results. According to both mean-field and two-site cluster treatments, the temperature-density phase diagrams of the model at zero external field are similar to those of the Ising lattice gas, but the effect of external field is quite different. In particular, at zero nonmagnetic attraction the field effect on the gas-liquid critical temperature becomes nonmonotonic. Having compared the field effects in the Ising, plane-rotator, and Heisenberg spin fluids, we conclude that the ability of the external field to decrease the gas-liquid critical temperature weakens with increasing number of spin components.