Density functional theory uses the electron density n(r), instead of the electronic wavefunction. We side-step the kinetic energy functional by constructing a thermodynamically equivalent classical map (CM). A classical Coulomb fluid whose zeroth-order pair-distribution function (PDF) g0(r) that agrees with the quantum g0, and interacting via a “Pauli exclusion potential” reproduces the thermodynamics of the electron fluid, when the classical-fluid temperature Tcf is chosen optimally. This Tcf is chosen so that the correlation energy of the classical fluid is the Kohn–Sham correlation energy. Then, the PDFs of the classical fluid closely agree with the PDFs of the two-dimensional (2D) and 3D uniform electron systems. Can we calculate sensitive Fermi-liquid properties (e.g., quasiparticle mass m*, Landé g-factor) of interacting electrons via this CM? Given the wide interest in the effective mass m* of electrons in 2D layers, we chose the 2D system for this study. Analytical and numerical results are used to define a partially regularized m* valid to logarithmic accuracy in the sense of Landau for the Hartree–Fock (H–F) approximation. The resulting H–F m* decreases linearly with the electron-disk radius rs. The m* including correlation is calculated via a physically transparent formula. This uses the CM of the 2D PDF and its finite-T exchange-correlation free energy Fxc(T). Our results for m* fall well within the results from recent quantum Monte-Carlo simulations at T = 0, and other theoretical and experimental results. © 2012 Wiley Periodicals, Inc.