Outside Gate A of the ExxonMobil oil refinery, the strike was fizzling.

Few had walked off the job. The complex was humming. As members of hard-left General Confederation of Labor gathered for a meeting, the event was crashed by counter-demonstrators.

"I want to be able to work," said Corinne Cavaille, 43, one of the 50-odd people who'd come to voice their opposition to the union, known by its French acronym CGT. Within an hour, the strike was off.

Despite all the disruption of this month's revolt against French labor reforms — fuel shortages, blocked bridges and street protests — there are signs that France's unions are losing power to mobilize workers. Some employees want less confrontational tactics, others worry about scaring away foreign employers.

For the CGT, the most militant of the two leading unions, it means that the fight against the government is also becoming a fight for relevance.

"It's been about 20 years since unions have forced a government to back down," said Stephane Sirot, a historian of the French labor movement at the University of Cergy-Pontoise. "If the movement finishes once more in failure, it might make further mobilization more complicated."

May's fight is centered on the Socialist government's slate of proposals aimed at loosening restrictions on working hours, layoffs and compensation — all in the hope of bringing extra flexibility to France's arthritic job market.

Talk to anyone in Le Havre, an industrial town ringed by container ports and oil refineries which have been wracked by industrial action, and you'd get any number of reasons for the anger that's disrupted the country: record arms sales to foreign governments, clampdowns on civil liberties and an overall sense that France's ruling Socialists have betrayed their base.

For France's biggest militant union, it's also a way to keep its sway over the country's politics.

"The CGT is losing steam," said Denis Jamet, a 65-year-old retiree making his way through Le Havre's unusually quiet city center Wednesday. "They're trying to stay relevant."

Only about 8 to 11 percent of the workforce in France is unionized. But their influence reaches beyond that, mainly through workplace elections of union representatives and the ability to negotiate industry-wide deals on behalf of non-unionized members. The recent ferment has a lot do with those elections, whose results are due in 2017, according to Dominique Andolfatto, a professor of political science at the University of Burgundy. The CGT, a union closely associated with the French Communist Party and the events of May 1968 — when the French government was nearly brought to its knees by a massive strike — is on the defensive in the face of gains by more dovish unions like French Confederation of Labor, known by its French acronym CFDT.

"These blockages are a sign of strength, but one can also argue that they're a sign of weakness," said Andolfatto. "If they were really that powerful they would do classic strikes, or massive protests. But they're having trouble mobilizing that many people."

Last week's debate outside the ExxonMobil gave some hint as to how globalization weighs against 1968-style action, even in a country with relatively modest levels of foreign direct investment. As strikers and counterdemonstrators hashed it out, one non-striker warned that "this refinery belongs to people in the United States. ... If we show this image, foreign companies are going to leave."

Another, who gave his name only as Denis, took the microphone to warn that the number of French refineries had fallen from 12 to only eight in the past decade.

"If you block the refinery every time you have a grievance how many more are going to be left?" he said.

The CGT and its allies have had more success elsewhere. Le Havre's oil terminal, responsible for 40 percent of France's oil imports, has been either completely or partially closed by strike action since last week. On Thursday, at least 10,000 people, led by striking dock workers and the CGT, descended on Le Havre's City Hall with a percussion band, powerful fireworks and paint bombs, decorating the grey, 1950s building with red-blue-and-yellow splatters.

"We're going back to '68," said Yamina Berriouche, a 46-year-old protester who struggled to make herself heard over the drums and the explosions. "People are angry."

Union-watchers say the fight between the CGT and the government is too close to call. On the one hand President Francois Hollande and his combative Prime Minister Manuel Valls are both unpopular and their reforms have divided the Socialist party. On the other hand, the more conciliatory CFDT has backed the reforms and many French people — like the Le Havre brasserie owner who said he'd like to go on strike against the strikers — are losing patience with the CGT and its mustachioed leader, Philippe Martinez.

Both sides have hinted at compromise in recent days as France's attention turns to the European Championship soccer tournament.

"Martinez is a big soccer fan," said Andolfatto, the academic. "He doesn't want to screw up the Euros."

If Hollande and Valls fold, it will leave the Socialist Party hobbling into next year's presidential election, when it will be challenged by the right-wing Republicans and the far-right National Front. But if the CGT fails to win the withdrawal of the reforms, it risks accelerating its slide into second place behind its CFDT rival and "consolidating a more practical-minded unionism," according to Andolfatto.

He was quick to caution that still wouldn't mean the disappearance of France's notorious strikes.

"There's a kind of revolutionary passion in France," said Andolfatto. "That won't be eradicated right away."

___

Raphael Satter can be reached at: http://raphaelsatter.com