PARIS—The French capital has fallen from grace as a bike-sharing paradise that inspired cities around the world to launch programs of their own.

Over the past six months, a project to upgrade Paris’s sprawling bike network has rendered it largely unusable. Gashes have appeared along the city’s sidewalks where docking stations have been uprooted. Seemingly serviceable bikes can’t be ridden because of electrical problems with newly installed stations. Overall the system, known as Velib’, is operating at a fraction of its former capacity.

The mess, dubbed an “industrial catastrophe” by French media, is casting a cloud over the city’s political leadership and dragging down the popularity of Anne Hidalgo, the Socialist mayor of Paris. Elected officials are learning a new lesson in big-city politics: Keep the local bike-sharing network up and rolling, or suffer the consequences.

“Hidalgo could pay dearly for this,” said Eric Azière, a Paris city councilor from a centrist party. “It has undermined her reputation for competence.”

Velib’ customers have been sharing stories of nonfunctioning bikes with the hashtag #Velibgate. On Saturday, one Twitter user posted a picture of a long row of Velib' bikes in their docking station, writing: “Not one works.”