We study the two-dimensional lattice multicomponent Abelian-Higgs model, which is a lattice compact U(1) gauge theory coupled with an -component complex scalar field, characterized by a global symmetry. In agreement with the Mermin-Wagner theorem, the model has only a disordered phase at finite temperature, and a critical behavior is observed only in the zero-temperature limit. The universal features are investigated by numerical analyses of the finite-size scaling behavior in the zero-temperature limit. The results show that the renormalization-group flow of the 2D lattice -component Abelian-Higgs model is asymptotically controlled by the infinite gauge-coupling fixed point, associated with the universality class of the 2D field theory.