Automatic segmentation of the left ventricle (LV) of a living human heart in a magnetic resonance (MR) image (2D+t) allows to measure some clinical significant indices like the regional wall thicknesses (RWT), cavity dimensions, cavity and myocardium areas, and cardiac phase. Here, we propose a novel framework made of a sequence of two fully convolutional networks (FCN). The first is a modified temporal-like VGG16 (the "localization network") and is used to localize roughly the LV (filled-in) epicardium position in each MR volume. The second FCN is a modified temporal-like VGG16 too, but devoted to segment the LV myocardium and cavity (the "segmentation network"). We evaluate the proposed method with 5-fold-cross-validation on the MICCAI 2019 LV Full Quantification Challenge dataset. For the network used to localize the epicardium, we obtain an average dice index of 0.8953 on validation set. For the segmentation network, we obtain an average dice index of 0.8664 on validation set (there, data augmentation is used). The mean absolute error (MAE) of average cavity and myocardium areas, dimensions, RWT are 114.77~mm²; 0.9220~mm; 0.9185~mm respectively. The computation time of the pipeline is less than 2~s for an entire 3D volume. The error rate of phase classification is 7.6364%, which indicates that the proposed approach has a promising performance to estimate all these parameters.