ABSTRACT The Fornax galaxy cluster is the richest nearby (D ∼ 20 Mpc) galaxy association in the southern sky. As such, it provides a wealth of opportunities to elucidate on the processes where environment holds a key role in transforming galaxies. Although it has been the focus of many studies, Fornax has never been explored with contiguous homogeneous wide-field imaging in 12 photometric narrow and broad bands like those provided by the Southern Photometric Local Universe Survey (S-PLUS). In this paper, we present the S-PLUS Fornax Project (S+FP) that aims to comprehensively analyse the galaxy content of the Fornax cluster using S-PLUS. Our data set consists of 106 S-PLUS wide-field frames (FoV∼1.4 × 1.4 deg2) observed in five Sloan Digital Sky Survey-like ugriz broad bands and seven narrow bands covering specific spectroscopic features like O ii, Ca ii H+K, Hδ, G band, Mg b triplet, Hα, and the Ca ii triplet. Based on S-PLUS specific automated photometry, aimed at correctly detecting Fornax galaxies and globular clusters in S-PLUS images, our data set provides the community with catalogues containing homogeneous 12-band photometry for ∼3 × 106 resolved and unresolved objects within a region extending over ∼208 deg2 (∼5 Rvir in RA) around Fornax’ central galaxy, NGC 1399. We further explore the eagle and IllustrisTNG cosmological simulations to identify 45 Fornax-like clusters and generate mock images on all 12 S-PLUS bands of these structures down to galaxies with M⋆ ≥ 108 M⊙. The S+FP data set we put forward in this first paper of a series will enable a variety of studies some of which are briefly presented.