By recording low-pressure absorption lines of N2O around 3.9 microm, we fully qualify a pulsed entangled-cavity doubly resonant optical parametric oscillator as a power tool for high-resolution spectroscopy. This compact source runs at a high repetition rate (>10 kHz) with a low threshold of oscillation (<8 microJ), is mode-hop-free tunable over 5 cm(-1), and displays single-frequency Fourier-transformed-limited operation (linewidth <0.005 cm(-1)). A high potential for nonlinear spectroscopy is also expected given the high peak power (70 W) and the good quality (M2 < 2) of the output beam.