Carlos Ghosn was long one of the most admired executives in the auto industry.

He was hailed as a corporate savior when the French automaker Renault bought a stake in Nissan and dispatched him to Japan on a rescue mission. He built a thriving global alliance between the two companies, and for 12 years he led both simultaneously.

“Carlos Ghosn did some great things,” said Scott Smith, the owner of four Nissan franchises in Georgia. “He gave us a lot of good product. He was the Lee Iacocca of Europe.”

Mr. Ghosn’s career was abruptly halted 14 months ago with his arrest in Japan on charges of financial wrongdoing. After an audacious escape from custody and a surreptitious trek to Lebanon, he declared that he was determined to restore his personal reputation. But however his legal troubles play out, there are growing questions about another aspect of his reputation: whether he left Nissan in good shape.

Less than three years after Mr. Ghosn gave up the top job at Nissan, it has slipped into a deep slump. Revenue and profits are falling in markets around the world. Sales in the United States — its most crucial market after China — fell 10 percent in 2019, a staggering decline at a time when auto sales are at near-record levels.