Sensorized insoles provide a tool for gait studies and health monitoring during daily life. For users to accept such insoles, they need to be comfortable and lightweight. Previous research has demonstrated that sensorized insoles can estimate ground reaction forces (GRFs). However, these insoles often assemble commercial components restricting design freedom and customization. Within this work, we incorporated four 3D-printed soft foam-like sensors to sensorize an insole. To test the insoles, we had nine participants walk on an instrumented treadmill. The four sensors behaved in line with the expected change in pressure distribution during the gait cycle. A subset of this data was used to identify personalized Hammerstein–Wiener (HW) models to estimate the 3D GRFs while the others were used for validation. In addition, the identified HW models showed the best estimation performance (on average root mean squared (RMS) error 9.3%, $ {R}^2 $=0.85 and mean absolute error (MAE) 7%) of the vertical, mediolateral, and anteroposterior GRFs, thereby showing that these sensors can estimate the resulting 3D force reasonably well. These results were comparable to or outperformed other works that used commercial force-sensing resistors with machine learning. Four participants participated in three trials over a week, which showed a decrease in estimation performance over time but stayed on average 11.35% RMS and 8.6% MAE after a week with the performance seeming consistent between days two and seven. These results show promise for using 3D-printed soft piezoresistive foam-like sensors with system identification regarding the viability for applications that require softness, lightweight, and customization such as wearable (force) sensors.