We present the addition of nebular emission from the narrow-line regions (NLR) surrounding active galactic nuclei (AGNs) to BEAGLE (BayEsian Analysis of GaLaxy sEds). Using a set of idealized spectra, we fit to a set of observables (emission-line ratios and fluxes) and test the retrieval of different physical parameters. We find that fitting to standard diagnostic-line ratios plus [O II] lambda 3726, lambda 3729/[O III] lambda 5007, H beta/H alpha, [O I] lambda 6300/[O II] lambda 3726, lambda 3729, and H alpha flux, degeneracies remain between dust-to-metal mass ratio (xi(NLR)(d)) and ionization parameter (U-s(NLR)) in the NLR gas, and between slope of the ionizing radiation (alpha(PL), characterizing the emission from the accretion disc around the central black hole) and total accretion-disc luminosity (L-acc). Since these degeneracies bias the retrieval of other parameters even at maximal signal-to-noise ratio (S/N), without additional observables, we suggest fixing alpha(PL) and dust-to-metal mass ratios in both NLR and H II regions. We explore the S/N in H beta required for un-biased estimates of physical parameters, finding that S/N(H beta) similar to 10 is sufficient to identify an NLR contribution, but that higher S/N is required for un-biased parameter retrieval (similar to 20 for NLR-dominated systems, similar to 30 for objects with approximately equal H beta contributions from NLR and H II regions). We also compare the predictions of our models for different line ratios to previously published models and data. By adding [He II] lambda 4686-line measurements to a set of published line fluxes for a sample of 463 AGN NLR, we show that our models with -4 < log logU(S)(NLR) < -1.5 can account for the full range of observed AGN properties in the local Universe.