Aims. In M dwarfs, optical emission lines and continua are sensitive to changing chromospheric conditions, e. g., during flares. To study flare conditions for an observed spectrum, a comparison to synthesised spectra from model atmospheres is needed. Methods. Using the stellar atmosphere code PHOENIX, we computed a set of 41 1D NLTE parameterised chromospheric models including the photosphere and parts of the transition region. By comparison of a linear combination of the synthesised spectra and a quiescent (observed) chromosphere to observed UVES/VLT spectra of a giant flare of the M 5.5 dwarf CN Leo (Gl406), we find the best-fitting flare model chromosphere. Results. Our model spectra give a fairly good overall description of the observed continua and emission lines. In the best-fitting model, the temperature minimum is deep in the atmosphere resulting in high electron pressure for the chromospheric flaring area. The inferred chromospheric filling factor of the flare is about 3 percent, which declines during the flare. The photospheric flare filling factor is about 0.3 percent.