We report the magnetotransport properties up to 7 T in the organic highly conducting Langmuir-Blodgett(LB) films formed by a molecular association of the electroactive donor molecule bis(ethylendioxy)tetrathiafulvalene (BEDO-TTF) and stearic acid CH$_3$(CH$_2$)$_{16}$COOH. We show the logarithmic decrease of dc conductivity and the negative transverse magnetoresistance at low temperature. They are interpreted in the weak localization of two-dimensional (2D) electronic system based on the homogeneous conducting layer with the molecular size thickness of BEDO-TTF. The electronic length with phase memory is given at the mesoscopic scale, which provides for the first time evidence of the 2D coherent charge transport in the conducting LB films.