In this Letter we consider spinless Fermi gases placed inside a cavity and study the critical strength of a pumping field for driving a superradiance transition. We emphasize that the Fermi surface nesting effect can strongly enhance the superradiance tendency. Around certain fillings, when the Fermi surface is nearly nested with a relevant nesting momentum, the susceptibility of the system toward a checkboard density-wave ordered state is greatly enhanced in comparison with a Bose gas with the same density, because of which a much smaller (sometime even vanishingly small) critical pumping field strength can give rise to superradiance. This effect leads to interesting reentrance behavior and a topologically distinct structure in the phase diagram. Away from these fillings, the Pauli exclusion principle brings about the dominant effect for which the critical pumping strength is lowered in the low-density regime and increased in the high-density regime. These results open the prospect of studying the rich phenomena of degenerate Fermi gases in a cavity.