  We estimate the He II to H I column density ratio, \eta = N(He II)/N(H I), in
the intergalactic medium towards the high redshift (z_{em} = 2.885) bright
quasar QSO HE 2347-4342 using Voigt-profile fitting of the H I transitions in
the Lyman series and the He II Lyman-$\alpha$ transition as observed by the
FUSE satellite. In agreement with previous studies, we find that $\eta > 50$ in
most of the Lyman-$\alpha$ forest except in four regions where it is much
smaller ($\eta \sim 10-20$) and therefore inconsistent with photo-ionization by
the UV background flux. We detect O VI and C IV absorption lines associated
with two of these regions ($z_{\rm abs}$ = 2.6346 and 2.6498). We show that if
we constrain the fit of the H I and/or He II absorption profiles with the
presence of metal components, we can accommodate $\eta$ values in the range
15-100 in these systems assuming broadening is intermediate between pure
thermal and pure turbulent. While simple photo-ionization models reproduce the
observed N(O VI)/N(C IV) ratio, they fail to produce low $\eta$ values contrary
to models with high temperature (i.e T $\ge 10^5$ K). The Doppler parameters
measured for different species suggest a multiphase nature of the absorbing
regions. Therefore, if low $\eta$ values were to be confirmed, we would favor a
multi-phase model in which most of the gas is at high temperature ($>$ 10$^5$
K) but the metals and in particular C IV are due to lower temperature ($\sim$
few $10^4$ K) photo-ionized gas.
