What would you do if you found out that the staff that you hired was a fraud?

I will inform the police immediately

Fraud in the work place might happened and should be dealt with it in immediate action yet after have enough evidence; also, remember that you shouldn't be emotionally driven either positive or negative.
there are some points I should think about first:
1- How this employee can affect the organization if he discovered my action? I should have preventative regulations immediately, like coordinate with the IT, security and audit department to have immediate preventative actions.
2- Does this action can affect my company goodwill? In some case, very few case the fraud employee might affect the organization goodwill like those who have direct communication with the customers, then I have deal with the matter with more caution.3-Does this employee is senior top manager? Such level if proved to be fraud the actions should be more strategic as it will be of direct impact on the organization goodwill and position in the market.

You can do several things including Informing the upper management , Freezing all financial transactions with the payroll department, at take legal actions by informing the company's lawyer.
But always remember to double check ! You don't want to make a mistake in such situations or else it would be extremely embarrassing and would destroy trust between the employees.