We obtained high-resolution Far Ultraviolet Spectroscopic Explorer (FUSE; R ∼ 20,000) and Very Large Telescope (VLT; R ∼ 45,000) spectra of the quasar HE 2347-4342 in order to study the properties of the intergalactic medium between redshifts z = 2.0 and 2.9. The high-quality optical spectrum allows us to identify approximately 850 H I absorption lines with column densities between N ∼ 5×1011 and 1018 cm-2. The reprocessed FUSE spectrum extends the wavelength coverage of the He II absorption down to an observed wavelength of 920 Å. Source flux is detected to rest-frame wavelengths as short as ∼237 Å. Approximately 1400 He II absorption lines are identified, including 917 He II Lyα systems and some of their He II Lyβ, Lyγ, and Lyδ counterparts. The ionization structure of He II is complex, with approximately 90 absorption lines that are not detected in the hydrogen spectrum. These features may represent the effect of soft ionizing sources. The ratio η = N(He II)/N(H I) varies approximately from unity to more than a thousand, with a median value of 62 and a distribution consistent with the intrinsic spectral indexes of quasars. This provides evidence that the dominant ionizing field is from the accumulated quasar radiation, with contributions from other soft sources such as star-forming regions and obscured active galactic nuclei, which do not ionize helium. We find an evolution in η toward smaller values at lower redshift, with the gradual disappearance of soft components. At redshifts z > 2.7, the large but finite increase in the He II opacity, τ = 5 ± 1, suggests that we are viewing the end stages of a reionization process that began at an earlier epoch. Fits of the absorption profiles of unblended lines indicate comparable velocities between hydrogen and He+ ions. For line widths bHe+He+ = ξbH, we find ξ = 0.95 ± 0.12, indicating a velocity field in the intergalactic medium dominated by turbulence. At hydrogen column densities N < 3 × 1012 cm-2, the number of forest lines shows a significant deficit relative to a power law and becomes negligible below N = 1011 cm-2.