The two main classes of liquid-crystal (LC) phases of rod-like molecules are nematics, where the rods align in the same direction (the nematic director, n), and smectics where the rods are not only aligned but also form layers. The electro-optic effects in LC devices that are a backbone in today's display industry, mainly use the Fréedericksz transition which is the bulk reorientation of a surface-anchored nematic by an electric field. Conventional (uniaxial) smectics do not present a Fréedericksz transition because, due to their layered structure, the director reorientation would distort the layers, which would cost too much energy. In a worldwide ongoing effort to extend the variety of LC compounds suitable for applications in the display industry, bent-shaped molecules have recently raised much attention, since they present multiple new LC phases with unusual properties. In this paper, we report on a structural and electro-optic study of the LC phases of a bent-shaped dimer. On cooling from the isotropic liquid, this compound shows a usual nematic (N), a twist-bend nematic (NTB), and a biaxial smectic-A phase (SmAb). Quite surprisingly, contrary to usual smectics, SmAb presents a remarkable electro-optic response, with low (<4 V) voltage threshold, no reorganization of the smectic layers, and low (<1 ms) response time (i.e., 30 times faster than the N phase at higher temperature). We interpret this unexpected electro-optic effect as a Fréedericksz transition affecting the secondary director m of the SmAb, and we model it by analogy with the usual Fréedericksz transition of the n director of the uniaxial N phase. Indeed, a Fréedericksz transition affecting only m in this biaxial fluid smectic does not alter its layered structure and costs little energy. From the point of view of applications, thanks to its low relaxation time, this “biaxial” Fréedericksz transition could be exploited in electro-optic devices that require fast switching.