  We present simultaneous measurements of Josephson inductance and DC transport
characteristics of ballistic Josephson junctions based upon an epitaxial
Al-InAs heterostructure. The Josephson inductance at finite current bias
directly reveals the current-phase relation. The proximity-induced gap, the
critical current and the average value of the transparency $\bar{\tau}$ are
extracted without need for phase bias, demonstrating, e.g.,~a near-unity value
of $\bar{\tau}=0.94$. Our method allows us to probe the devices deeply in the
non-dissipative regime, where ordinary transport measurements are featureless.
In perpendicular magnetic field the junctions show a nearly perfect Fraunhofer
pattern of the critical current, which is insensitive to the value of
$\bar{\tau}$. In contrast, the signature of supercurrent interference in the
inductance turns out to be extremely sensitive to $\bar{\tau}$.
