In this paper, we present a first measurement of Brillouin gain spectrum with dual-frequency solid-state laser. This allows a coherent detection of the Brillouin backscattered spectrum in a frequency range below the hundreds of MHz by fine tuning of the difference between the two cross-polarized fields emitted by the laser. The photodetection at low frequency benefits from the balanced detection technique where high dynamic range measurements are largely available. The narrow linewidth of the cross-polarized filed permits also the direct measurement of the Brillouin spectrum linewidth. The system is demonstrated by measuring the Brillouin frequency shift with temperature when standard single-mode fiber (SMF-28) and large effective area fiber (LEAF) are fully heated. This gives temperature coefficients close to theoretical expectations with values of 1.16 MHz/°C for SMF-28 and 1.15 MHz/°C for LEAF.