The majority of traditional eddy current-based metal film thickness measurement systems measure the thickness of the metal film by detecting changes in the impedance or voltage of the detection coil, leading to limited measurement range and susceptibility to measurement errors caused by variations in lift-off distance. This article proposes a method for metal film thickness measurement across a wide range using a high-performance magnetoelectric (ME) sensor to directly detect the total magnetic field of the excitation field and the induced field. Numerical calculations based on the eddy current magnetic field model reveal a highly linear relationship within a specific range between this total magnetic field and the logarithm of the metal film thickness. If the detectable magnetic field range of the magnetic field sensor covers 32–51 nT with a bandwidth of up to 1.5 MHz, theoretically, the measurement of copper film thickness within the range of 0.65 nm–1000 $\mu$ m can be achieved by adjusting the excitation magnetic field frequency, and the measurement error introduced by the lift-off distance can also be ignored. The experimentally prepared ME sensor, covering a range of 30 pT–100 nT within a bandwidth of 1.5 kHz–1.5 MHz, was used to construct a metal film thickness measurement system. Measurements on copper films with thicknesses ranging from nanometers to micrometers, under excitation fields at six different frequency excitation fields within the range of 1.5 kHz–1.5 MHz, exhibited measurement errors within 1%, confirming the feasibility of this method for a wide range of copper film thicknesses from 60 nm–350 $\mu$ m.