We report on a search for the optical counterparts of 175-μm selected sources from the Far-Infrared Background (FIRBACK) survey in the European Large Area ISO Survey (ELAIS) N2 field. Applying a likelihood ratio technique to optical catalogues from the Isaac Newton Telescope - Wide Field Survey (INT-WFS), we found optical identifications for 33 out of 55 FIRBACK sources in this field. These were then reassessed in the light of associations with the ELAIS final catalogue for the N2 field, to yield a final set of 31 associations. We have investigated the nature of this population through a comparison of their observed spectral energy distributions (SEDs) with predictions from radiative transfer models which simulate the emission from both cirrus and starburst components. We find the far-infrared sources to be 80 per cent starburst galaxies with their starburst component at a high optical depth. The resulting SEDs were used to estimate far-infrared luminosities, star formation rates (SFRs), dust temperatures and dust masses. The N2 FIRBACK population is found to consist of four suspected ultraluminous infrared galaxies (ULIRGs) with LFIR~ 1012Lsolar and SFRFIR > 100Msolaryr-1, a number of luminous infrared galaxies (LIRGs) with moderate star formation rates and LFIR~ 1011Lsolar and a population of low-redshift quiescently star-forming galaxies. We also discuss the implications of these results for current evolutionary models.