We explore the connection between the kinematics, structures and stellar populations of massive galaxies at 0.6<z<1.0 using the fundamental plane (FP). Combining stellar kinematic data from the Large Early Galaxy Astrophysics Census (LEGA-C) survey with structural parameters measured from deep Hubble Space Telescope imaging, we obtain a sample of 1419 massive (log(M_*_/M_{sun}_)>10.5) galaxies that span a wide range in morphology, star formation activity, and environment, and therefore is representative of the massive galaxy population at z~0.8. We find that quiescent and star-forming galaxies occupy the parameter space of the g-band FP differently and thus have different distributions in the dynamical mass-to-light ratio (M_dyn_/L_g_), largely owing to differences in the stellar age and recent star formation history, and to a lesser extent, the effects of dust attenuation. In contrast, we show that both star-forming and quiescent galaxies lie on the same mass FP at z~0.8, with a comparable level of intrinsic scatter about the plane. We examine the variation in M_dyn_/M_*_ through the thickness of the mass FP, finding no significant residual correlations with stellar population properties, Sersic index, or galaxy overdensity. Our results suggest that, at fixed size and velocity dispersion, the variations in M_dyn_/L_g_ of massive galaxies reflect an approximately equal contribution of variations in M_*_/L_g_, and variations in the dark matter fraction or initial mass function.