We report the second study from the FUSE survey of molecular hydrogen in translucent clouds for the line of sight toward HD 110432. This star lies beyond the Coalsack dark nebula, and, with E(B-V) = 0.40 and A_V = 1.32, this line of sight bridges the gap between less-extinguished diffuse-cloud lines of sight with A_V ~ 1, such as ζ Ophiuchi, and translucent-cloud lines of sight with A_V 2, such as HD 73882. Through profile fitting and a curve-of-growth analysis, we have derived rotational populations for H₂ for J = 0-7. The line of sight has a total molecular hydrogen column density, log N(H₂) = 20.68 ± 0.05 cm^-2, nearly identical to that toward ζ Oph but a factor of 3 less than that toward HD 73882. The ratio of N(J = 1) to N(J = 0) yields a kinetic temperature T_kin = 63 ± 7 K, which is similar to other lines of sight with A_V 1. The high-J lines show considerable excitation above this temperature. However, the high-J lines cannot be well fitted to a single excitation temperature, and the even-J lines of para-hydrogen appear slightly enhanced relative to the odd-J lines of ortho-hydrogen. The high-J excitation is similar to that toward ζ Oph but is much smaller than that toward HD 73882. Chemical modeling indicates that the physical conditions in the cloud(s) are very similar to those in the cloud(s) toward ζ Oph. An analysis of IUE spectra of the Lyα line gives N(H I) = 20.85 ± 0.15 cm^-2. Combined with N(H₂), we derive a hydrogen molecular fraction, f = 0.58 ± 0.12, statistically identical to that found for the lines of sight toward ζ Oph and HD 73882. From the FUSE data and a curve-of-growth analysis using the same component structure as H₂, we find log N(HD) = 15.2 cm^-2, which is between the values found for ζ Oph and HD 73882. Profile fitting suggests smaller b values for HD than for H₂, and log N(HD) = 16.0 cm^-2. From FUSE and IUE data, we derive log N(CO) ≈ 14.3 cm^-2, assuming the same component structure as CH or log N(CO) ≈ 14.8 cm^-2, if all observed CO is cospatial with the strongest CH component. From the combined measurements of hydrogen- and carbon-containing molecules, the line of sight toward HD 110432 appears quite similar to the diffuse-cloud line of sight toward ζ Oph and quite dissimilar to the translucent-cloud line of sight toward HD 73882. Upcoming FUSE observations will further explore the transition between diffuse and translucent clouds.