  The physics potential of EDELWEISS detectors for the search of low-mass
Weakly Interacting Massive Particles (WIMPs) is studied. Using a data-driven
background model, projected exclusion limits are computed using frequentist and
multivariate analysis approaches, namely profile likelihood and boosted
decision tree. Both current and achievable experimental performance are
considered. The optimal strategy for detector optimization depends critically
on whether the emphasis is put on WIMP masses below or above $\sim$ 5
GeV/c$^2$. The projected sensitivity for the next phase of the EDELWEISS-III
experiment at the Modane Underground Laboratory (LSM) for low-mass WIMP search
is presented. By 2018 an upper limit on the spin-independent WIMP-nucleon
cross-section of $\sigma_{SI} = 7 \times 10^{-42}$ cm$^2$ is expected for a
WIMP mass in the range 2$-$5 GeV/c$^2$. The requirements for a future
hundred-kilogram scale experiment designed to reach the bounds imposed by the
coherent scattering of solar neutrinos are also described. By improving the
ionization resolution down to 50 eV$_{ee}$, we show that such an experiment
installed in an even lower background environment (e.g. at SNOLAB) should allow
to observe about 80 $^8$B neutrino events after discrimination.
