Magnetoelectric (ME) magnetic field sensors utilize ME effects in ferroelectric ferromagnetic layered heterostructures to convert magnetic signals into electrical signals. However, the substrate clamping effect greatly limits the design and fabrication of ME composites with high ME coefficients. To reduce the clamping effect and improve the ME response, a flexible ME sensor based on PbZr0.2Ti0.8O3 (PZT)/CoFe2O4 (CFO) ME bilayered heterostructure was deposited on mica substrates via van der Waals oxide heteroepitaxy. A saturated magnetization of 114.5 emu/cm3 was observed in the bilayers. The flexible sensor exhibited a strong ME coefficient of 6.12 V/cm·Oe. The local ME coupling has been confirmed by the evolution of the ferroelectric domain under applied magnetic fields. The flexible ME sensor possessed a stable response with high sensitivity to both AC and DC weak magnetic fields. A high linearity of 0.9988 and sensitivity of 72.65 mV/Oe of the ME sensor were obtained under flat states. The ME output and limit-of-detection under different bending states showed an inferior trend as the bending radius increased. A flexible proximity sensor has been demonstrated, indicating a promising avenue for wearable device applications and significantly broadening the potential application of the flexible ME magnetic field sensors.