Ro-vibrational spectra of the $\nu_3$ and $\nu_6$ bands of chloromethane ($\mathrm{CH_3Cl}$) were recorded in the 650--1130 $\mathrm{cm}^{-1}$ range using a Fourier transform spectrometer at the AILES beamline of the SOLEIL synchrotron facility. Two isotopologues ($\mathrm{CH_3^{35}Cl}$ and $\mathrm{CH_3^{37}Cl}$) have been analyzed with the tensorial formalism developed in Dijon and a total of 6753 lines were assigned. We derived 23 tensorial parameters for the lines positions (4 for the ground state, 6 for $\nu_3$, and 13 for $\nu_6$), and 7 for the lines intensities (4 for $\nu_3$, 3 for $\nu_6$). From those parameters and self-broadening coefficients found in the literature, we simulated spectra of both isotopologues. The derived parameters were converted in the Watson formalism to be compared with a previous study. Using these results, we set up a new database of calculated chloromethane spectral lines (ChMeCaSDa).