Circuit to run a 3 phase magnet generator as motor?
It should be possible to use 3 hall cell magnetic field detectors to provide commutation sensing. There are numerous IC's that accept 3 hall inputs and provide motor drive signals.
Which is most appropriate depends on the alternator / motor ratings.
eg the controllers in "hover boards" usually use 3 hall sensors and  will drive motors in the hundreds of watts range at voltages typically around 40V - but this could be altered. 

What power / voltage / current / RPM do you expect to be dealing with?

Do you have a brand, part number, photo or related web link?