  Dynamic conductance spectra are taken from Au/CeCoIn$_5$ point contacts in
the Sharvin limit along the (001) and (110) directions. Our conductance
spectra, reproducibly obtained over wide ranges of temperature, constitute the
cleanest data sets ever reported for HFSs. A signature for the emerging
heavy-fermion liquid is evidenced by the development of the asymmetry in the
background in the normal state. Below $T_c$, an enhancement of the sub-gap
conductance arising from Andreev reflection is observed, with the magnitude of
$\sim$ 13.3 % and $\sim$ 11.8 % for the (001) and the (110) point contacts,
respectively, an order of magnitude smaller than those observed in conventional
superconductors but consistent with those in other HFSs. Our zero-bias
conductance data for the (001) point contacts are best fit with the extended
BTK model using the d-wave order parameter. The fit to the full conductance
curve of the (001) point contact indicates the strong coupling nature
($2\Delta/k_{B}T_c = 4.64$). However, our observed suppression of both the
Andreev reflection signal and the energy gap indicates the failure of existing
models. We provide possible directions for theoretical formulations of the
electronic transport across an N/HFS interface. Several qualitative features
observed in the (110) point contacts provide the first clear spectroscopic
evidence for the $d_{x^2-y^2}$ symmetry.
