The customer would be arrested by the police, then he/she would be subject to a trial and IF actually found guilty would be sentenced to - say - six months of jail.

If he/she had actually killed someone, then he/she would probably get thirty years or a life sentence.

But here we are still talking about someone who (BTW presumably in good faith) presented the "wrong" piece of paper (a fake bill that he maybe got as change from another restaurant) at the counter of your restaurant to pay the bill, and that was (again presumably) ready to give you another "good" banknote to pay for the service.

I don't think (actually hope) the restaurant owner would call the police for this.