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PARIS — France’s self-styled political road warriors may finally be running out of road.

Since their weekly protests began more than three months ago, the “yellow vests” have fought their way to a rare kind of popularity, straddling France’s political spectrum with a broad, populist message that blames establishment elites for the country’s high cost of living.

But with polls showing that popularity beginning to wane, the movement faces an existential challenge: Translating their outdoor enthusiasm into indoor political power.

A masked "yellow vest" protester makes the victory sign near a burning barricade in Paris on Dec. 1. Abdulmonam Eassa / AFP - Getty Images file

Their prospects are complicated by the same contradictions that earned them such wide appeal.

Prominent members within the movement claim the "yellow vests" are leaderless even as they behave like leaders themselves. They have attracted support from the far-left and the far-right — longstanding and bitter rivals for French public opinion.

Even more confounding, the "yellow vests" claim to be apolitical even as they make political demands.

“It’s contradictory,” said Thierry Paul Valette, a wiry and well-coiffed actor and author who has emerged as a kind of leader alongside several other prominent protesters.

Early this month, Valette became the latest "yellow vest" activist to launch a political party to represent the movement in European Parliament elections scheduled for May.

Thierry Paul Valette during a protest in Paris earlier this month. Abaca Press / Sipa USA via AP file

“In a sense it’s against a political system,” he said. “But also starting an under-the-radar political movement, because when you have meetings with deputies and ministers and even a president, we’re already in a political action.”

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The movement is named after the reflective garments all French motorists are required to carry. Its demands initially focused on lowering taxes, particularly for gas.

But after President Emmanuel Macron scrapped a proposed diesel tax, the protests continued and the demonstrators' demands appeared to shift, variously pushing for the president’s resignation, public referendums for government decisions and still lower taxes.

That such a group has earned recognition from the political powers-that-be is a sign of the times. The "yellow vests" are the latest sighting of a loosely affiliated populist trend that has pushed voters throughout the Western world, on both the right and left, away from incumbent parties and ideologies toward identity politics and non-traditional candidates, normally by vilifying perceived elites.

“The 'yellow vests' are probably the purest example of the populism we’ve been seeing throughout the world,” said Dr. Angelos Chryssogelos, an expert on populist movements at Harvard University. “But the same thing that has made them popular will also be a problem for them because it will prevent them from forming a political party.”

Unlike populist causes that have scored election victories on the right, such as the election of President Donald Trump in 2016, or on the left, such as the rise of British Labour Party leader Jeremy Corbyn, the "yellow vests" lack a strong connection to either political side, Chryssogelos said.

And even though the group began as right-leaning rejection of Macron’s pro-environment tax on diesel, recent protests have featured Communist flags and anti-capitalist chants. Various members describe themselves as “apolitical,” “transpolitical,” and “anti-establishment.”

The group’s refusal to nominate leaders is so pervasive among protesters that some self-appointed leaders who attempted to run for public office have reported receiving death threats from other members.

So far, four separate political parties with different agendas have formed out the "yellow vest" protests.

“I don’t think that the 'yellow vests' can find a way to gather to form a political party,” said Jean-Jacques Guillet, the mayor of the well-off Paris suburb of Chaville.

Guillet and other political leaders had convened at a community center one recent Saturday for a “great debate” — a series of mild-mannered town halls organized by Macron as a kind of answer to the protesters' complaint that the people are alienated from politics.

Guillet compared the "yellow vests" to eczema — a skin rash that comes and goes.

"Yellow vest" protesters are showered by a water cannon during clashes with police in Bordeaux, France, on Saturday. Georges Gobet / AFP - Getty Images

“I think it’s wrong to think that there can be a real lasting political movement for the 'yellow vests,'” he said.

However dismissive of the "yellow vests," the French public may be shifting in Guillet’s direction.

February is the first month when more than half of respondents to a national poll commissioned by BFMTV said they wanted the protests to stop.

But "yellow vest" stalwarts believe the French public are still behind them.

Jerome Rodrigues, one of the leaderless movement’s unofficial leaders, may lose vision in one of his eyes after police struck him with an LBD 40, a kind of crowd control grenade that Rodrigues calls a “weapon of war.”

Already known for his signature fedora and imposing beard, Rodrigues’s wound has made him into a kind of social media martyr among protesters. But Rodrigues, like his cohorts, has his own unique version of the movement's political agenda.

Rodrigues said the "yellow vests" demand three basic goals: lowering taxes, reorganizing France’s political system so that democracy is more direct, and granting fewer privileges for those in government, such as official vehicles and funerals paid for by the state.

Jerome Rodrigues is one of the leading figures of the "yellow vest" movement. ERIC FEFERBERG / AFP - Getty Images

Yet Rodrigues’ main preoccupation seemed to be with Macron, a former investment banker who styles himself as a liberal centrist but is seen by many "yellow vests" as elitist.

"Macron, well, he breaks everything," he said. "He tells everyone to go home because he is the boss. This is unacceptable.”