The James Webb Space Telescope ( JWST ) will provide deep imaging and spectroscopy for sources at redshifts above 6 , covering the entire Epoch of Reionization ( EoR , 6 < z < 10 ) , and enabling the detailed exploration of the nature of the different sources during the first 1 Gyr of the history of the Universe . The Medium Resolution Spectrograph ( MRS ) of the mid-IR Instrument ( MIRI ) will be the only instrument on board JWST able to observe the brightest optical emission lines H \alpha and [ OIII ] 0.5007 \mu m at redshifts above 7 and 9 , respectively , providing key insights into the physical properties of sources during the early phases of the EoR . This paper presents a study of the H \alpha fluxes predicted by state-of-the-art FIRSTLIGHT cosmological simulations for galaxies at redshifts of 6.5 to 10.5 , and its detectability with MIRI . Deep ( 40 ksec ) spectroscopic integrations with MRS will be able to detect ( S/N > 5 ) EoR sources at redshifts above 7 with intrinsic star formation rates ( SFR ) of more than 2 M _ { \odot } yr ^ { -1 } , and stellar masses above 4-9 \times 10 ^ { 7 } M _ { \odot } . These limits cover the upper end of the SFR and stellar mass distribution at those redshifts , representing \sim 6 % and \sim 1 % of the predicted FIRSTLIGHT population at the 6.5-7.5 and 7.5-8.5 redshift ranges , respectively . In addition , the paper presents realistic MRS simulated observations of the expected rest-frame optical and near-infrared spectra for some spectroscopically confirmed EoR sources recently detected by ALMA as [ OIII ] 88 \mu m emitters . The MRS simulated spectra cover a wide range of low metallicities from about 0.2 to 0.02 Z _ { \odot } , and different [ OIII ] 88 \mu m/ [ OIII ] 0.5007 \mu m line ratios . The simulated 10ks MRS spectra show S/N in the range of 5 to 90 for H \beta , [ OIII ] 0.4959,0.5007 \mu m , H \alpha and HeI1.083 \mu m emission lines of the currently highest spectroscopically confirmed EoR ( lensed ) source MACS1149-JD1 at a redshift of 9.11 , independent of metallicity . In addition , deep 40 ksec simulated spectra of the luminous merger candidate B14-65666 at 7.15 shows the MRS capabilities of detecting , or putting strong upper limits on , the weak [ NII ] 0.6584 \mu m , [ SII ] 0.6717,0.6731 \mu m , and [ SIII ] 0.9069,0.9532 \mu m emission lines . These observations will provide the opportunity of deriving accurate metallicities in bright EoR sources using the full range of rest-frame optical emission lines up to 1 \mu m. In summary , MRS will enable the detailed study of key physical properties such as internal extinction , instantaneous star formation , hardness of the ionizing continuum , and metallicity in bright ( intrinsic or lensed ) EoR sources .