We present analysis from simultaneous FUSE , ASCA , and EUVE observations , as well as a reanalysis of archival HST spectra , from the extreme Narrow-line Seyfert 1 Galaxy RE 1034 + 39 ( KUG 1031 + 398 ) . RE 1034 + 39 has an unusually hard spectral energy distribution ( SED ) that peaks in the soft X-rays . Its emission lines are unusual in that they can all be modelled as a Lorentzian centered at the rest wavelength with only a small range in velocity widths . In order to investigate whether the unusual SED influences the emission line ratios and equivalent widths , we present three complementary types of photoionization analysis . The FUSE spectrum was particularly important because it includes the high-ionization line O vi . First , we use the photoionization code Cloudy and the SED developed from the coordinated observations to confirm that the emission lines are consistent with observed hard SED . The best model parameters were an ionization parameter \log ( U ) \approx - 2 and a hydrogen number density \log ( n _ { H } ) = 9.75 [ cm ^ { -2 } ] . Second , we present a Locally Optimally-emitting Cloud model . This model produced enhanced O vi as observed , but also yielded far too strong Mg ii . Third , we develop a series of semi-empirical SEDs , run Cloudy models , and compare the results with the measured values using a figure of merit ( FOM ) . The FOM minimum indicates similar SED and gas properties as were inferred from the one-zone model using the RE 1034 + 39 continuum . Furthermore , the FOM increases sharply toward softer continua , indicating that a hard SED is required by the data in the context of a one-zone model .