  Estimating metallicity of classical Cepheids is of prime importance for
studying metallicity effect on stellar evolution, chemical evolution of
galaxies, and ultimately its impact on period-luminosity relation used in the
extragalactic distance scale. We aim at establishing new empirical relations
for estimating the iron content of classical Cepheids for short and
long-periods based on Fourier parameters from the $V$-band light curves. We
calibrate new interrelations of Fourier parameters to convert $V$-band
empirical relations into the $I$-band. Then we apply these relation in $V$ and
$I$-bands to Cepheids from Milky Way (MW), Small and Large Magellanic Clouds
(SMC and LMC) available in the literature. Last, we map the metallicity
distribution in these galaxies for investigating potential application in
galactic archeology. These empirical relations in $V$ and $I$ bands are able to
derive the mean metallicity of a sample of MW, SMC and LMC Cepheids in
agreement with literature values within 1$\sigma$. We also show that these
relations are precise enough to reconstruct the radial metallicity gradients
within the MW from OGLE data. The empirical relations in the $V$ and $I$ bands
calibrated in this paper for short and long-period Cepheids provide a new
useful tool to estimate the metallicity of Cepheids which are not accessible by
spectroscopy. The calibration can be improved with further high-resolution
spectroscopic observations of metal-poor Cepheids and homogeneous photometries
in $V$ and $I$ bands.
