We present a characterization of the binary protostar system that is forming within a dense core in the isolated dark cloud BHR71. The pair of protostars, IRS1 and IRS2, are both in the Class 0 phase, determined from observations that resolve the sources from 1 μm out to 250 μm and from 1.3 mm to 1.3 cm. The resolved observations enable the luminosities of IRS1 and IRS2 to be independently measured (14.7 and 1.7 L, respectively), in addition to the bolometric temperatures 68 K and 38 K, respectively. The surrounding core was mapped in NH₃ (1, 1) with the Parkes radio telescope, and followed with higher-resolution observations from ATCA in NH₃ (1, 1) and 1.3 cm continuum. The protostars were then further characterized with ALMA observations in the 1.3 mm continuum along with N₂D⁺ (), ¹²CO, ¹³CO, and C¹⁸O () molecular lines. The Parkes observations find evidence for a velocity gradient across the core surrounding the two protostars, while ATCA reveals more complex velocity structure toward the protostars within the large-scale gradient. The ALMA observations then reveal that the two protostars are at the same velocity in C¹⁸O, and N₂D⁺ exhibits a similar velocity structure as NH₃. However, the C¹⁸O kinematics reveal that the rotation on scales <1000 au around IRS1 and IRS2 are in opposite directions. Taken with the lack of a systematic velocity difference between the pair, it is unlikely that their formation resulted from rotational fragmentation. We instead conclude that the binary system most likely formed via turbulent fragmentation of the core.