We present simultaneous Nuclear Spectroscopic Telescope Array (NuSTAR ) and Suzaku observations of the X-ray binary Cygnus X-1 in the hard state. This is the first time this state has been observed in Cyg X-1 with NuSTAR, which enables us to study the reflection and broadband spectra in unprecedented detail. We confirm that the iron line cannot be fit with a combination of narrow lines and absorption features, instead requiring a relativistically blurred profile in combination with a narrow line and absorption from the companion wind. We use the reflection models of Garci´a et al. to simultaneously measure the black hole spin, disk inner radius, and coronal height in a self-consistent manner. Detailed fits to the iron line profile indicate a high level of relativistic blurring, indicative of reflection from the inner accretion disk. We find a high spin, a small inner disk radius, and a low source height and rule out truncation to greater than three gravitational radii at the 3σ confidence level. In addition, we find that the line profile has not changed greatly in the switch from soft to hard states, and that the differences are consistent with changes in the underlying reflection spectrum rather than the relativistic blurring. We find that the blurring parameters are consistent when fitting either just the iron line or the entire broadband spectrum, which is well modeled with a Comptonized continuum plus reflection model.