  We present time-domain THz spectroscopy of thin films of the heavy-fermion
superconductor CeCoIn$_5$. The complex optical conductivity is analyzed through
a Drude model and extended Drude model analysis. Below the $\approx$ 40 K Kondo
coherence temperature, a narrow Drude-like peak forms, as the result of the $f$
orbital - conduction electron hybridization and the formation of the
heavy-fermion state. Via an extended Drude model analysis, we measure the
frequency-dependent scattering rate ($1/ \tau $) and effective mass
($m^*/m_b$). This scattering rate shows a linear dependence on temperature,
which matches the dependence of the resistivity as expected. Nonetheless, the
width of the low-frequency Drude peak (characterized by a {\it renormalized}
quasiparticle scattering rate ($1 / \tau^* = m_b/ m^* \tau $) does show a $T^2$
dependence giving evidence for a hidden Fermi state.
