  We estimate effective temperature ($T_{\rm eff}$), stellar radius, and
luminosity for a sample of 271 M-dwarf stars (M0V-M7V) observed as a part of
CARMENES (Calar Alto high-Resolution search for M dwarfs with Exo-earths with
Near-infrared and optical Echelle Spectrographs) radial-velocity planet survey.
For the first time, using the simultaneously observed high resolution
(R$\sim90000$) spectra in the optical (0.52 - 0.96 $\mu$m) and near-infrared
(0.96 - 1.71 $\mu$m) bands, we derive empirical calibration relationships to
estimate the fundamental parameters of these low-mass stars. We select a sample
of nearby and bright M-dwarfs as our calibrators for which the physical
parameters are acquired from high-precision interferometric measurements. To
identify the most suitable indicators of $T_{\rm eff}$, radius, and luminosity
(log $L/L_{\odot}$), we inspect a range of spectral features and assess them
for reliable correlations. We perform multivariate linear regression and find
that the combination of pseudo equivalent widths and equivalent width ratios of
the Ca II at 0.854 $\mu$m and Ca II at 0.866 $\mu$m lines in the optical and
the Mg I line at 1.57 $\mu$m in the NIR give the best fitting linear functional
relations for the stellar parameters with root mean square errors (RMSE) of
99K, 0.06 $R_{\odot}$ and 0.22 dex respectively. We also explore and compare
our results with literature values obtained using other different methods for
the same sample of M dwarfs.
