The idea is, I have a fast spinning magnet and next to it a wire (with 2 free ends). When the + pole is next to the wire it will attract the electrons, and when the - pole is by the wire it will repulse them, creating alternating current.
You should be able to induce AC current in the wire, but you may need to change its orientation.
Electrons move along electrical field lines, not along magnetic field lines. The lines of an electric field induced by a changing magnetic field are generally normal to the lines of the magnetic field.
Therefore, you should get better results, if the wire is turned $90^\circ$ and goes through the page.