We present a theoretical overview and experimental demonstration of a continuous-wave, cavity-enhanced optical absorption spectrometry method to detect molecular gas. This technique utilizes the two non-degenerate polarization modes of a birefringent cavity to obtain a zero background readout of the intra-cavity absorption. We use a double-pass equilateral triangle optical cavity design with additional feed-forward frequency noise correction to measure the R14e absorption line in the 30012←00001 band of CO2 at 1572.655 nm. We demonstrate a shot noise equivalent absorption of 3 × 10−13 cm−1 Hz−1/2.