FLORENCE, Italy — Eike Schmidt, the new director of the Uffizi Gallery here and the first non-Italian to hold the job, took what seemed a logical step. In the spring, he set up loudspeakers warning visitors about scalpers and pickpockets who target tourists waiting in the perennially long lines outside Italy’s most-visited museum, famous for its magnificent treasures by Botticelli and Raphael.

But not everyone was grateful. A few days later, three Florence police officers with local media in tow arrived at his desk and handed him a fine of about $329, for broadcasting without proper city authorization. “Initially I was a little bit angry,” Mr. Schmidt, a German art historian, said recently over a glass of wine. But he quickly spotted an opportunity, telling them he would pay the fine out of his own pocket. The next day, when he did, journalists were there snapping photos, making him an instant local celebrity.

Florentines began approaching Mr. Schmidt on the street to express their support. “Some initially said: ‘Don’t stop. Finally someone takes these problems seriously,’” Mr. Schmidt said. “There are other people who actually try to give me money,” he added with a laugh. Once seen as a naïve foreigner, he had earned public respect.

The clashing reactions to the loudspeaker experiment point to a fundamental challenge facing Mr. Schmidt. As he fights to manage the crowds, generate more revenue and improve the museum experience — including its chaotic ticketing system and long lines — will he continue to marshal popular support and prevail against a morass of bureaucratic restraints, vested interests and political intrigue?