Deep Convolutional Neural Networks (CNNs) achieve high accuracy but often rely on purely global, gradient-based optimisation, which can lead to overfitting, redundant filters, and reduced interpretability. To address these limitations, we propose NM-Hebb, a two-phase training framework that integrates neuro-inspired local plasticity with distance-aware supervision. Phase 1 extends standard supervised training by jointly optimising a cross-entropy objective with two biologically inspired mechanisms: (i) a Hebbian regulariser that aligns the spatial mean of activations with the mean of the corresponding convolutional filter weights, encouraging structured, reusable primitives; and (ii) a learnable neuromodulator that gates an elastic-weight-style consolidation loss, preserving beneficial parameters without freezing the network. Phase 2 fine-tunes the backbone with a pairwise metric-learning loss, explicitly compressing intra-class distances and enlarging inter-class margins in the embedding space. Evaluated on CIFAR-10, CIFAR-100, and TinyImageNet across five backbones (ResNet-18, VGG-11, MobileNet-v2, EfficientNet-V2, DenseNet-121), NM-Hebb achieves consistent gains over baseline and other methods: Top-1 accuracy improves by +2.0-10.0 pp (CIFAR-10), +2.0-9.0 pp (CIFAR-100), and up to +4.3-8.9 pp (TinyImageNet), with Normalised Mutual Information (NMI) increased by up to +0.15. Qualitative visualisations and filter-level analyses further confirm that NM-Hebb produces more structured and selective features, yielding tighter and more interpretable class clusters. Overall, coupling local Hebbian plasticity with metric-based fine-tuning yields CNNs that are not only more accurate but also more interpretable, offering practical benefits for resource-constrained and safety-critical AI deployments.