A classical gauge model based on the Lie group SU(3)_L X U(1)_N with exotic quarks is reformulated within the formalism of non-associative geometry associated to an L-cycle. The N charges of the fermionic particles and the related parameters constraints are uniquely determinedalgebraic consequences. Moreover, the number of scalar particles are dictated by the non-associativity of the geometry. As a byproduct of this formalism, the scalar, charged and neutral gauge bosons masses as well as the mixing angles are derived. Furthermore, various expressions of the vector and axial couplings of the quarks and leptons with the neutral gauge bosons and lower bounds of the very heavy gauge bosons are also obtained.