We report a measurement of the branching fraction of the decay B0-->D(*+)D(*-) and of the CP-odd component of its final state using the BABAR detector. With data corresponding to an integrated luminosity of 20.4 fb (-1) collected at the Upsilon(4S) resonance during 1999-2000, we have reconstructed 38 candidate signal events in the mode B0-->D(*+)D(*-) with an estimated background of 6.2+/-0.5 events. From these events, we determine the branching fraction to be B(B0-->D(*+)D(*-))=[8.3+/-1.6(stat)+/-1.2(syst)]x10(-4). The measured CP-odd fraction of the final state is 0.22+/-0.18(stat)+/-0.03(syst).