James II? Unknown. James I? Yes.
That´s not right. James I was only a Member of the Order of the Phoenix, noz an Auror. He had inherited enough money, so didn´t need a job.
James was a pure blood wizard who inherited a lot of wealth. So much so, his family could live on it without needing to work. Upon joining the Order of the Phoenix, he decided to devote his life to it, and so did not have a job. Its implied he also helped to support Lupin and Sirius, since Lupin couldn't find much work as a werewolf, and Sirius had been disowned and cut off from his family fortune. At least until his mother had died.