The ejecta velocities of type-Ia supernovae (SNe Ia), as measured by the Si II $lambda 6355$ line, have been shown to correlate with other supernova properties, including color and standardized luminosity. We investigate these results using the Foundation Supernova Survey, with a spectroscopic data release presented here, and photometry analyzed with the SALT2 light-curve fitter. We find that the Foundation data do not show significant evidence for an offset in color between SNe Ia with high and normal photospheric velocities, with $Delta c = 0.005 pm 0.014$. Our SALT2 analysis does show evidence for redder high-velocity SN Ia in other samples, including objects from the Carnegie Supernova Project, with a combined sample yielding $Delta c = 0.017 pm 0.007$. When split on velocity, the Foundation SN Ia also do not show a significant difference in Hubble diagram residual, $Delta HR = 0.015 pm 0.049$ mag. Intriguingly, we find that SN Ia ejecta velocity information may be gleaned from photometry, particularly in redder optical bands. For high-redshift SN Ia, these rest-frame red wavelengths will be observed by the Nancy Grace Roman Space Telescope. Our results also confirm previous work that SN Ia host-galaxy stellar mass is strongly correlated with ejecta velocity: high-velocity SN Ia are found nearly exclusively in high-stellar-mass hosts. However, host-galaxy properties alone do not explain velocity-dependent differences in supernova colors and luminosities across samples. Measuring and understanding the connection between intrinsic explosion properties and supernova environments, across cosmic time, will be important for precision cosmology with SNe Ia.
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