TIMBUKTU, Mali — France’s president, François Hollande, paid a triumphant visit to this ancient city on Saturday, receiving a rapturous welcome from thousands of people who gathered next to a 14th-century mosque to dance, play drums and chant “Vive la France!” The muezzin, whose singing calls residents to pray five times a day, wore a scarf in the colors of the French flag as he shouted, “Vive Hollande!”

It had the trappings of a “mission accomplished” moment.

But even as people outside the mud-and-wood mosque hailed the French leader as the city’s, and their country’s, savior, questions remain about what France has accomplished aside from chasing Islamic extremists from the cities and into their desert and mountain redoubts.

“These Islamists, they have not been defeated,” said Moustapha Ben Essayouti, a member of one of the city’s most prominent families who lined up to greet Mr. Hollande here. “Hardly any of them have been killed. They have run into the desert and the mountains to hide.”

Even Mr. Hollande, who praised French and Malian troops gathered here for accomplishing “an exceptional mission,” acknowledged that “the fight is not over.”