Two-dimensional QCD with <math><msub><mi>N</mi><mi>c</mi></msub></math> colors and <math><msub><mi>N</mi><mi>f</mi></msub></math> flavors of massless fermions in the fundamental representation is expected to exhibit conformal behavior in the infrared governed by a <math><mi>u</mi><mo>(</mo><msub><mi>N</mi><mi>f</mi></msub><mo>)</mo></math> Wess–Zumino–Witten model with level <math><msub><mi>N</mi><mi>c</mi></msub></math>. Using numerical analysis within the lattice formalism with exactly massless overlap fermions, we show the emergence of such behavior in the infrared limit. Both the continuum extrapolated low-lying eigenvalues of the massless Dirac operator and the propagator of scalar mesons exhibit a flow from the ultraviolet to the infrared. We find that the amplitude of the conserved current correlator remains invariant under the flow, while the amplitude of the scalar correlator approaches <math><msub><mi>N</mi><mi>f</mi></msub></math>-independent values in the infrared.