Motivated by the possibility of pressure-induced exciton condensation in intermediate-valence Tm[Se,Te] compounds we study the Falicov-Kimball model with finite f-hole valence and c-electron conduction bandwidths. Depending on the system parameters the local interband Coulomb attraction may establish coherence between c- and f-states, leading to an excitonic insulator phase at low temperatures. We find strong evidence that the excitonic insulator typifies either a BCS condensate of electron-hole pairs (weak-coupling regime) or a Bose-Einstein condensate (BEC) of preformed excitons (strong-coupling regime), which points towards a BCS-BEC transition scenario as Coulomb correlations increase in the extended Falicov-Kimball model.