We present Raman studies of graphene films grown on copper foil by atmospheric pressure CVD with n-decane as a precursor, a mixture of nitrogen and hydrogen as the carrier gas, under different hydrogen flow rates. A novel approach for the processing of the Raman spectroscopy data was employed. It was found that in particular cases, the various parameters of the Raman spectra can be assigned to fractions of the films with different thicknesses. In particular, such quantities as the full width at half maximum of the 2D peak and the position of the 2D graphene band were successfully applied for the elaborated approach. Both the G- and 2D-band positions of single layer fractions were blue-shifted, which could be associated with the nitrogen doping of studied films. The XPS study revealed the characteristics of incorporated nitrogen, which was found to have a binding energy around 402 eV. Moreover, based on the statistical analysis of spectral parameters and the observation of a G-resonance, the twisted nature of the double-layer fraction of graphene grown with a lower hydrogen feeding rate was demonstrated. The impact of the varied hydrogen flow rate on the structural properties of graphene and the nitrogen concentration is also discussed.