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.
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