The party, well aware of its relative strengths and limitations, made a conscious decision in 2012 to focus on specific towns in the 2014 elections. In the newsmagazine Le Nouvel Observateur, Nicolas Lebourg — a French historian who studied party documents related to the training of activists and political interns — laid out the party’s calculation: towns were easier to win than cities but would still garner much attention from the news media. The National Front clearly hoped that the visibility of any elected mayors would help the party shed the longstanding stereotype of its typical member: an old guy in a leather jacket, longing for the glory days of France’s colonial past, cracking jokes about Arabs and Jews, with little real interest in the tedium of managing a budget. The last time the National Front had several mayors elected, in the 1990s, two of the four became embroiled in widely ­publicized legal cases while still in office. This time around, the mayors were expected to do better. “Professionalization and entrenchment,” Lebourg wrote, “were the two words that kept coming up in regards to the 2014 local elections.”

One year into their jobs, the mayors have received extensive press, not all of it good. In Hayange, a steel-manufacturing town in the northeast, the new mayor, Fabien Engelmann, became the object of media controversy when his office sent a halal butcher, who prepares meat according to Muslim law, a letter insisting that he abide by the frequently flouted rule requiring shops to stay closed on Sunday mornings. That same mayor’s office also informed a dance teacher hoping to rent space for a North African-style dance class that she could not do so, on the grounds that the class was “incompatible with the National Front.” And according to a fellow member of the National Front working in his office, the mayor asked if there was a way to move local merchants of Arab descent farther from the center of town. (The mayor has denied this.) Engelmann is now contesting charges of campaign-finance violations.

Rachline, by contrast, seems determined to be noticed only as a paragon of professionalism. His campaign questioned the building of the town’s mosque, but he is no longer standing in its way. He implemented standard, but relatively uncontroversial, National Front policies — cutting a social-­service organization’s funds, increasing the local police force. Two or three armed officers now stand conspicuously outside the mayor’s office, which looks onto an open square with a medieval cathedral on one side.

Rachline was fortunate to have run for office at a moment when the town was in need of a strong manager, if not a savior. Fréjus was in financial crisis when he started his campaign. “We’re the fifth-most-indebted town in France,” I heard from almost every resident I spoke to.

At an outdoor bar just up the street from the mayor’s office, Christine Bertolo, a 60-year-old retired housekeeper, was drinking with three friends. They all happily volunteered that they had voted National Front in the mayoral elections and would most likely vote for Le Pen in 2017. Bertolo — who described herself as “disgusted” by her country’s mainstream politicians — characterized Fréjus as a microcosm of France. The former mayor was charged with corruption (also true of Sarkozy), municipal finances were terrible (France’s economic growth is lagging) and the quality of life was in steep decline (a complaint heard nationwide). “For 30 years, all the mayors, on the left and on the right, they’ve been filling their pockets,” Bertolo said. “And we’re the ones who fall through the holes.”

She said what people often say before they admit to voting for the Front: “I’m not racist, but. . . . ” What comes next is usually one of the following: “something has to change,” “the cost of living is too high,” “the politicians have done nothing,” “we have too much immigration.” Or, in Bertolo’s case, “they have lost our trust.” She meant the politicians: Hollande has not delivered on his campaign promise to increase taxes on the rich, spending much of his political capital instead on marriage rights for gay couples; Sarkozy, on the right, alienated the working class and was captured on camera telling a farmer to “shove off” (with an added epithet). Possibly, Bertolo said, Le Pen would be better; she could not be worse.