This paper proposes a magnetoelectric (ME) composite transducer structure consisting of a magnetostrictive H-type Fe-Ni fork substrate and piezoelectric PZT plates. The fork composite structure has a higher ME voltage coefficient compared to other ME composite structures due to the higher quality (Q) factor. The ME sensitivity of the fork structure reaches 12 V/Oe (i.e., 150 V/cm Oe). The fork composite with two PZT plates electrically connected in series exhibits over 5 times higher ME voltage coefficient than the output of the rectangle structure in the same size. The experiment shows the composite of a Fe-Ni fork substrate and PZT plates has a significantly enhanced ME voltage coefficient and a higher ME sensitivity relative to the prior sandwiched composite laminates. By the use of a lock-in amplifier with 10 nV resolution, this transducer can detect a weak magnetic field of less than $10^{-12}$ T. This transducer can also be designed for a magnetoelectric energy harvester due to its passive high-efficiency ME energy conversion.