PARIS — One protest movement started a year ago in France and drew hundreds of thousands at its peak to roundabouts across the country in angry “Yellow Vest” demonstrations against planned increases in gas taxes.

Another — a nationwide strike expressing fury over President Emmanuel Macron’s plans to overhaul the pension system — began this past week. On Saturday, it continued to paralyze parts of the country.

Even as the strength of the long-running Yellow Vest protests has dissipated over the year, the movement’s simmering anger at the president has run smack dab this weekend into the latest turmoil over his pension plans.

Both events have harnessed broader discontent with the policies of Mr. Macron, who is viewed both by both Yellow Vests and labor activists as arrogant and disconnected from their daily struggles. At their most violent, the Yellow Vest protests saw people break shop windows, the police fire tear gas and rubber bullets and Mr. Macron consider a state of emergency.