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 $bar{tau}$.
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