A complex Langevin framework is described for carrying out numerical simulations of coupled field equations for flow and structure of inhomogeneous polymeric fluids. The formalism permits an exact embedding of the relevant thermodynamic forces into the dynamical equations, regardless of the characteristic length scale of the inhomogeneities in the fluid. As such, it is capable of treating a wide variety of systems, such as dilute and semidilute polymer solutions, microemulsions, block copolymers, and micellar solutions, including those whose equilibrium properties and self-assembly characteristics are not well described by mean-field theory. The formalism also integrates with existing molecular and continuum descriptions of coupled stress and species concentration dynamics. In this report, we present the method for the simplest case of a homopolymer solution.