The new law is aimed at making tourist attractions, including the Martin Luther King Jr. National Historic Site, more welcoming for tourists.
Opponents included activists for the poor and civil rights groups, who complained the ordinance is a mean-spirited attempt to hide homeless people.
City council deliberations this summer inspired noisy protests, and Franklin signed the proposal Friday without making a public appearance.
Under the ordinance, beggars get a warning on the first offence and referred to social services on the second. They can do a short time in jail if they get three citations in one year.
The ordinance also outlines tougher rules for beggars citywide, making it a crime to ask for money at night or near train stations or ATMs.