Under the condition that the local-field effects in photonic crystals have been considered, a field average method based on the effective medium theory was used to calculate the effective linear refractive index of a two-dimensional triangle-lattice photonic crystal in the first band. The calculated refractive index agrees well with that obtained directly by using the plane-wave expansion method. Furthermore, a slow-light enhancement factor was introduced to calculate the effective nonlinear refractive index coefficients. The calculated nonlinear coefficients of the photonic crystal is strongly dispersive: the nonlinear coefficient decreases slowly to the minimum and then goes up quickly. The frequency-dependent nonlinear coefficients directly demonstrate that the local-field effect and slow light effect influence the nonlinear effects in the photonic crystals simultaneously. The results may be helpful for tuning the nonlinear effects by using man-made microstructures.