  We report the complex dielectric function of the quasi-one-dimensional
chalcogenide Ta$_2$NiSe$_5$, which exhibits a structural phase transition that
has been attributed to exciton condensation below $T_c = 326$ K, and of the
isostructural Ta$_2$NiS$_5$ which does not exhibit such a transition. Using
spectroscopic ellipsometry, we have detected exciton doublets with pronounced
Fano lineshapes in both the compounds. The exciton Fano resonances in
Ta$_2$NiSe$_5$ display an order of magnitude higher intensity than those in
Ta$_2$NiS$_5$. In conjunction with prior theoretical work by E. Rashba, we
attribute this observation to the giant oscillator strength of spatially
extended exciton-phonon bound states in Ta$_2$NiSe$_5$. The formation of
exciton-phonon complexes in Ta$_2$NiS$_5$ and Ta$_2$NiSe$_5$ is confirmed by
the pronounced temperature dependence of sharp interband transitions in the
optical spectra, whose peak energies and widths scale with the thermal
population of optical phonon modes. The description of the optically excited
states in terms of strongly overlapping exciton complexes is in good agreement
with the hypothesis of an EI ground state.
