  Milky Way Cepheid variables with accurate {\it Hubble Space Telescope}
photometry have been established as standards for primary calibration of the
cosmic distance ladder to achieve a percent-level determination of the Hubble
constant ($H_0$). These 75 Cepheid standards are the fundamental sample for
investigation of possible residual systematics in the local $H_0$ determination
due to metallicity effects on their period-luminosity relations. We obtained
new high-resolution ($R\sim81,000$), high signal-to-noise ($S/N\sim50-150$)
multi-epoch spectra of 42 out of 75 Cepheid standards using ESPaDOnS instrument
at the 3.6-m Canada-France-Hawaii Telescope. Our spectroscopic metallicity
measurements are in good agreement with the literature values with systematic
differences up to $0.1$ dex due to different metallicity scales. We homogenized
and updated the spectroscopic metallicities of all 75 Milky Way Cepheid
standards and derived their multiwavelength ($GVIJHK_s$)
period-luminosity-metallicity and period-Wesenheit-metallicity relations using
the latest {\it Gaia} parallaxes. The metallicity coefficients of these
empirically calibrated relations exhibit large uncertainties due to low
statistics and a narrow metallicity range ($\Delta\textrm{[Fe/H]}=0.6$~dex).
These metallicity coefficients are up to three times better constrained if we
include Cepheids in the Large Magellanic Cloud and range between $-0.21\pm0.07$
and $-0.43\pm0.06$ mag/dex. The updated spectroscopic metallicities of these
Milky Way Cepheid standards were used in the Cepheid-Supernovae distance ladder
formalism to determine $H_0=72.9~\pm 1.0$\textrm{~km~s$^{-1}$~Mpc$^{-1}$},
suggesting little variation ($\sim 0.1$ ~km~s$^{-1}$~Mpc$^{-1}$) in the local
$H_0$ measurements due to different Cepheid metallicity scales.
