  Starting from a higher Courant bracket associated to exceptional generalized
geometry, we provide a systematic derivation of all types of fluxes and their
Bianchi identities for four-dimensional compactifications of M-theory. We show
that these fluxes may be understood as generalized Wess-Zumino terms in certain
topological threebrane sigma-models of AKSZ-type, which relates them to the
higher structure of a Lie algebroid up to homotopy. This includes geometric
compactifications of M-theory with G-flux and on twisted tori, and also its
compactifications with non-geometric Q- and R-fluxes in specific
representations of the U-duality group SL(5) in exceptional field theory.
