The semileptonic decay of the neutral K meson, K0L → π± e∓ ν (Ke3 ), was used to study the strangeness-changing weak interaction of hadrons. A sample of 5.6 million reconstructed events recorded by the NA48 experiment was used to measure the Dalitz plot density. Admitting all possible Lorentz-covariant couplings, the form factors for vector (f+(q2)), scalar (fS) and tensor (fT) interactions were measured. The linear slope of the vector form factor λ+ = 0.0284 ± 0.0007 ± 0.0013 and values for the ratios |fS/f+(0)| = 0.015 +0.007-0.010 ± 0.012 and |fT/f+(0)| = 0.05 +0.03-0.04 ± 0.03 were obtained. The values for fS and fT are consistent with zero. Assuming only vector–axial-vector couplings, λ+ = 0.0288 ± 0.0004 ± 0.0011 and a good fit consistent with pure V–A couplings were obtained. Alternatively, a fit to a dipole form factor yields a pole mass of M = 859 ± 18 MeV, consistent with the K∗(892) mass.