The electric field is E=−dVdx
If V=0, we can not say E must be zero, we say only E may be zero.
If V≠0, E must be zero when V is max i.e, dVdx=0 For example, inside the conductor E=0, but V≠0
If E≠0 , V may be zero when two equal and opposite charges separated by a distance and at the midpoint in between the charges field is non-zero but potential is zero.