We present a theoretical study of the induced transient birefringence of a low density homogeneous molecular gas in a resonant pump-probe experiment, The molecular coherent state induced by the resonant pump field is described by second-order perturbation theory. The induced birefringence can be detected by a delayed probe pulse propagating through the molecular medium after illumination by the pump pulse. In the case of a nonresonant probe, the birefringence is linearly proportional to the mean value of the electronic polarizability of the molecular gas. The birefringence signal is composed of distinct components due to population change and those of rotational, vibrational, and mixed vibrational-rotational origins. This is demonstrated by numerical simulations on Li-2 gas. Moreover, the quantum beats contained in the birefringence, as a function of the time delay between the pump and probe pulses, is dominated by the pure rotational motion. Finally, the birefringence is sensitive to the shape of the applied pump pulse and dependent on the spectral phase of the pump pulse.