We present new photometric and spectroscopic data of the dwarf planet Eris obtained on 2006 October and 2007 December with the Very Large Telescopes at ESO, Chile. We use three different instruments (FORS, ISAAC, and SINFONI) covering the 0.4-2.4 μm wavelength range. We show that N2 ice is not directly detected, but the wavelength positions of the bands of CH4 measured on the complete wavelength range seem to indicate that, as already suggested by Brown et al. and Licandro et al., a part of CH4 ice is diluted in N2. Spectral modeling using the Hapke theory reveals that a segregation of small and large particles of methane ice could exist on the surface. The presence of water ice and nitrogen is not completely excluded even if the respective absorption bands of these ices have not been directly detected. We present in this paper our methods to determine the wavelength shifts of the methane bands and the chemical composition from spectral modeling.