The Herschel Fornax Cluster Survey is a deep, far-infrared (FIR) survey of the Fornax cluster. The survey is in five Herschel bands (100-500 mu m) and covers an area of 16 deg(2) centred on NGC 1399. This paper presents photometry, detection rates, dust masses, and temperatures using an optically selected sample from the Fornax Cluster Catalogue. Our results are compared with those previously obtained using data from the Herschel Virgo Cluster Survey (HeViCS). In Fornax, we detect 30 of the 237 (13 per cent) optically selected galaxies in at least one Herschel band. The global detection rates are significantly lower than Virgo, reflecting the morphological make up of each cluster - Fornax has a lower fraction of late-type galaxies. For galaxies detected in at least three bands, we fitted a modified blackbody with a beta = 2 emissivity. Detected early-type galaxies (E/S0) have a mean dust mass, temperature, and dust-to-stars ratio of log(10)(\textless M-dust \textgreater/M-circle dot) = 5.82 +/- 0.20, \textless T-dust \textgreater = 20.82 +/- 1.77 K, and log(10) (M-dust/M-stars) = -3.87 +/- 0.28, respectively. Late-type galaxies (Sa to Sd) have a mean dust mass, temperature, and dust-to-stars ratio of log(10)(\textless M-dust \textgreater/M-circle dot) = 6.54 +/- 0.19, \textless T-dust \textgreater = 17.47 +/- 0.97 K, and log(10)(M-dust/M-stars) = -2.93 +/- 0.09, respectively. The different cluster environments seem to have had little effect on the FIR properties of the galaxies and so we conclude that any environment-dependent evolution has taken place before the cluster was assembled.