Brightest cluster galaxies (BCGs) in the cores of galaxy clusters have distinctly different properties from other low-redshift massive ellipticals. The majority of the BCGs in cool-core clusters show signs of active star formation. We present observations of NGC 4696, the BCG of the Centaurus galaxy cluster, at far-infrared (FIR) wavelengths with the Herschel space telescope. Using the PACS spectrometer, we detect the two strongest coolants of the interstellar medium, C ii at 157.74 μm and O i at 63.18 μm, and in addition N ii at 121.90 μm. The C ii emission is extended over a region of 7 kpc with a similar spatial morphology and kinematics to the optical Hα emission. This has the profound implication that the optical hydrogen recombination line, Hα, the optical forbidden lines, N ii λ6583 Å, the soft X-ray filaments and the FIR C ii line all have the same energy source. We also detect dust emission using the PACS and SPIRE photometers at all six wavebands. We perform a detailed spectral energy distribution fitting using a two-component modified blackbody function and find a cold 19-K dust component with mass 1.6 × 106 M⊙ and a warm 46-K dust component with mass 4.0 × 103 M⊙. The total FIR luminosity between 8 and 1000 μm is 7.5 × 108 L⊙, which using Kennicutt relation yields a low star formation rate of 0.13 M⊙ yr−1. This value is consistent with values derived from other tracers, such as ultraviolet emission. Combining the spectroscopic and photometric results together with optical Hα, we model emitting clouds consisting of photodissociation regions adjacent to ionized regions. We show that in addition to old and young stellar populations, there is another source of energy, such as cosmic rays, shocks or reconnection diffusion, required to excite the Hα and C ii filaments.