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We study the mixed formulation of the abstract Hodge Laplacian on axisymmetric domains with general data through Fourier finite element methods (Fourier-FEMs) in weighted function spaces. Closed Hilbert complexes and commuting projectors are used as in the work of Arnold, Falk & Winther, (2010, Finite element exterior calculus: from Hodge theory to numerical stability. Bull. Amer. Math. Soc. (N.S.) , 47 , 281–354), by using the new family of finite element spaces for general axisymmetric problems introduced in Oh, (2015, de Rham complexes arising from Fourier-FEMs in axisymmetric domains. Comput. Math. Appl. , 70 , 2063–2073). In order to get stability results and error estimates for the discrete mixed formulation, we construct commuting projectors that can be applied to functions with low regularity. [ABSTRACT FROM AUTHOR]