This paper presents observations of Cygnus A at 74 and 327 MHz at angular resolutions of approximately 10 and 3, respectively. These observations are among the highest angular resolutions obtained below 1000 MHz for this object. While the angular resolution at 74 MHz is not sufficient to separate clearly the hot spots from the lobes, guided by 151 and 327 MHz images, we have estimated the 74 MHz emission from the hot spots. We confirm that the emission from both the western and eastern hot spots flattens at low frequencies and that there is a spectral asymmetry between the two. For the eastern hot spot, a low-energy cutoff in the electron energy spectrum appears to explain the flattening, which implies a cutoff Lorentz factor gamma_min ~ 300, though we cannot exclude the possibility that there might be a moderate level of free-free absorption. For the western hot spot, the current observations are not sufficient to distinguish between a free-free absorped power-law spectrum and a synchrotron self-absorbed spectrum.