  Electron fraction and cosmic-ray ionization rates (CRIR) in star-forming
regions are important quantities in astrochemical modeling and are critical to
the degree of coupling between neutrals, ions, and electrons, which regulates
the dynamics of the magnetic field. However, these are difficult quantities to
estimate. We aim to derive the electron fraction and CRIR maps of an active
star-forming region. We combined observations of the nearby NGC 1333
star-forming region carried out with the NOEMA interferometer and IRAM 30-m
single dish to generate high spatial dynamic range maps of different molecular
transitions. We used the DCO$^+$ and H$^{13}$CO$^+$ ratio (in addition to
complementary data) to estimate the electron fraction and produce cosmic-ray
ionization rate maps. We derived the first large-area electron fraction and
CRIR resolved maps in a star-forming region, with typical values of $10^{-6.5}$
and $10^{-16.5}$ s$^{-1}$, respectively. The maps present clear evidence of
enhanced values around embedded young stellar objects (YSOs). This provides
strong evidence for locally accelerated cosmic rays. We also found a strong
enhancement toward the northwest region in the map that might be related either
to an interaction with a bubble or to locally generated cosmic rays by YSOs. We
used the typical electron fraction and derived a MHD turbulence dissipation
scale of 0.054 pc, which could be tested with future observations. We found a
higher cosmic-ray ionization rate compared to the canonical value for $N({\rm
H_2})=10^{21}-10^{23}$ cm$^{-2}$ of $10^{-17}$ s$^{-1}$ in the region, and it
is likely generated by the accreting YSOs. The high value of the electron
fraction suggests that new disks will form from gas in the ideal-MHD limit.
This indicates that local enhancements of $\zeta({\rm H_2})$, due to YSOs,
should be taken into account in the analysis of clustered star formation.
