PARIS — President Emmanuel Macron of France is facing the toughest crisis of his leadership after three weeks of violent protests across the country. “Yellow Vest” demonstrators have demanded that the government give financial relief to large parts of the population that are struggling to make ends meet.

Prime Minister Edouard Philippe sought to calm the furor on Tuesday by suspending a planned fuel tax increase for six months, reversing a policy that had set off the revolt.

But it’s not apparent that this single concession can clear the streets.

The Yellow Vest movement — whose followers wear or display high-visibility vests used in emergencies — has morphed into a collective outcry over deeper problems that have plagued France for years: declining living standards and eroding purchasing power. Both of which have worsened in the aftermath of Europe’s long-running financial crisis.