Aims. The distance of NGC 1316, the brightest galaxy in the Fornax cluster, provides an interesting test for the cosmological distance scale. First, because Fornax is the second largest cluster of galaxies within ≲25 Mpc after Virgo and, in contrast to Virgo, has a small line-of-sight depth; and second, because NGC 1316 is the single galaxy with the largest number of detected Type Ia supernovae (SNe Ia), giving the opportunity to test the consistency of SNe Ia distances both internally and against other distance indicators. Methods. We measure surface brightness fluctuations (SBF) in NGC 1316 from ground- and space-based imaging data. The sample provides a homogeneous set of measurements over a wide wavelength interval. The SBF magnitudes, coupled with empirical and theoretical absolute SBF calibrations, are used to estimate the distance to the galaxy. We also present the first B-band SBF measurements of NGC 1316 and use them together with the optical and near-IR SBF data to analyze the properties of field stars in the galaxy. Results. We obtain mag, or d = 20.8 ± 0.5(stat.) ± 1.5(sys.) Mpc. When placed in a consistent Cepheid distance scale, our result agrees with the distances from other indicators. On the other hand, our distance is ~17% larger than the most recent estimate based on SNe Ia. Possible explanations for this disagreement are the uncertain level of internal extinction, and/or calibration issues. Concerning the stellar population analysis, we confirm the results from other spectro-photometric indicators: the field stars in NGC 1316 are dominated by a component with roughly solar metallicity and intermediate age. A non-negligible mismatch exists between B-band SBF models and data. We confirm that such behavior can be accounted for by an enhanced percentage of hot horizontal branch stars. Conclusions. Our study of the SBF distance to NGC 1316, and the comparison with distances from other indicators, raises some concern about the homogeneity between the calibrations of different indicators. If not properly placed in the same reference scale, significant differences can occur, with dramatic impact on the cosmological distance ladder. Our results on the stellar populations properties show that SBF data over a broad wavelength interval are an efficient means of studying the properties of unresolved systems in peculiar cases like NGC 1316.