The molecular field-coupled nanocompunting (molFCN) technology encodes the information in the charge distribution of electrostatically coupled molecules, making it an exciting solution for future beyond-CMOS low-power electronics. Recent literature has shown that multi-molecule molFCN enables the design of devices with tailored unconventional characteristics, such as majority voters working as artificial neurons. This work presents a multi-molecule molFCN neuron model based on the weighted-inputs formulation to estimate molFCN neurons behavior. Then, the introduced model is used to design each neuron of molFCN circuits working as neural networks. In particular, we propose a molFCN neural network operating as an input pattern classifier. The results show the model aptitude in predicting the logic output values for individual neurons and, consequently, entire networks. The model accuracy has been evaluated by comparing the results from the neuron mathematical model with those obtained from the circuit-level simulations conducted with the SCERPA tool. Overall, this study highlights the strategic use of diverse molecules in molFCN layouts, customizing circuit operations, and expanding design possibilities for specific molFCN device functioning.