The ejecta velocities of Type Ia supernovae (SNe Ia), as measured by the SiII{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=0.004+/-0.015. Our SALT2 analysis does show evidence for redder high-velocity SNe Ia in other samples, including objects from the Carnegie Supernova Project, with a combined sample yielding {Delta}c=0.018+/-0.008. When split on velocity, the Foundation SNe Ia also do not show a significant difference in Hubble diagram residual, {Delta}HR=0.015+/-0.049mag. Intriguingly, we find that SN Ia ejecta velocity information may be gleaned from photometry, particularly in redder optical bands. For high-redshift SNe Ia, these rest-frame red wavelengths will be observed by the Nancy Grace Roman Space Telescope. Our results are in line with previous work that suggests SN Ia host-galaxy stellar mass is correlated with ejecta velocity: high-velocity SNe 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.