Netflix doesn’t qualify as a solo offender when it comes to Gallic stereotypes, as three musical theater works on the city’s stages show.PARIS — There’s been no shortage of complaints from Parisians about the Netflix series “Emily in Paris.” Yet an endless stream of clichés about the city — from cafes by the Louvre to chain smoking and ménages à trois — isn’t merely the province of Americans. French artists indulge, too; at home, however, rose-tinted nostalgia hits differently.Musical theater has been a frequent offender, and recently, mythical visions of Paris have been on offer at two rival playhouses. At the Théâtre du Châtelet, the city often felt like the protagonist of “Cole Porter in Paris,” a musical set in the 1920s; the Théâtre des Champs-Élysées roped the designer Christian Lacroix into lending period glamour to Jacques Offenbach’s operetta “La Vie Parisienne” (“Parisian Life”).And the stereotypes woven into their fabrics, by and large, are the same. Luxury fashion? Check. Casual philandering? Check. Entitled members of the bourgeoisie? Check.“Cole Porter in Paris,” especially, is an odd offering. Created and directed by Christophe Mirambeau, it is a jukebox musical of Porter hits. The songs are uneasily stitched into a plot about the years the composer spent in the French capital, from 1917 to 1928. His love for the city ran deep: Porter’s first Broadway hit was called simply “Paris,” and he often turned to this formative period for inspiration after his return to the United States.Mirambeau draws from Porter’s large oeuvre — inserting only George and Ira Gershwin’s “The Man I Love” as a bonus — to conjure nostalgic visions from les années folles (“the crazy years,” as the 1920s are known in French). The result is a breathless tour of a decade of French culture, filtered through an American sensibility and repackaged.The World of ‘Emily in Paris’The Netflix show, starring Lily Collins in the role of an American social media wiz in the French capital, is back for a second season. Emily, C’est Moi: As an American in Paris, our critic used to look down on Emily. He then realized they have more in common than he thought. Emily’s Closet: The show was derided for its unrealistic approach to French dressing. These looks define the upcoming season.The French Reaction: The response of actual Parisians to the first season was “ridicule” — French for ridiculous and absurd, as well as amusing.The Man Behind the Show: Darren Star, who also created “Sex and the City,” has specialized in escapist visions of the urban female experience.“I love Paris every moment,” three singers inform us in the opening number, drawn from Porter’s 1953 musical, “Can-Can.” The backdrop then rises to reveal the Eiffel Tower. When Linda Lee Thomas, Porter’s future wife, appears, she immediately launches into “You Don’t Know Paree,” first heard in “Fifty Million Frenchmen,” in 1929. (“Paree” appears in the title of three more of the evening’s songs.)With 29 numbers, the production is a musical marathon, which explains why the role of Porter is shared by three performers (Richard Delestre, Yoni Amar and Matthieu Michard). The orchestra Les Frivolités Parisiennes, which specializes in French comic opera from the 19th and 20th centuries, provided rousing backing onstage throughout.But who is the target audience? More often than not, Porter’s life serves as a flimsy excuse to flit from number to number and to drop the names of cultural figures like the impresario Serge Diaghilev and the dancer and club owner Ada “Bricktop” Smith. And for Parisians, there is something alienating about uncritical re-enactments of a perceived Golden Age.Rodolphe Briand, left, as Gardefeu and Laurent Deleuil as Bobinet in “La Vie Parisienne,” directed by Christian Lacroix at the Théâtre des Champs-Élysées.Marie PétryParisian mythmaking is typically centered around a handful of eras, and at the Théâtre des Champs-Élysées, “La Vie Parisienne” harks back to an earlier one: the Second Empire, which lasted from 1852 to 1870. At the time, Napoleon III gave Georges-Eugène Haussmann free rein to rebuild the capital, driving rapid growth. In that context, Offenbach’s 1866 operetta aimed to portray the real lives of (some) Parisians — namely, two dandies, Gardefeu and Bobinet, who can’t decide whether to focus their attentions on promiscuous demimondaines or respectable society ladies.Offenbach both celebrates and satirizes their lifestyle. Their entanglements with two Danish characters, the Baron and Baroness Gondremarck, show aspects of the city’s growing international appeal. The Baroness seeks cultural thrills; the Baron is more interested in becoming acquainted with the aforementioned demimondaines.“La Vie Parisienne” is the directing debut of Lacroix, the designer, whom the playbill describes as a “born nostalgic.” Over the past four decades, he has created costumes for a long list of operas, ballets and plays, often drawing on original sources. A keen historian, he looked to period fashion as well as to some of the 1866 designs for “La Vie Parisienne’s” premiere, and the result is luxurious.For lovers of Offenbach, there is an additional thrill. With the help of researchers from the Palazzetto Bru Zane, a Venice-based music center, the production restores portions of the score that were cut because the original cast protested their difficulty. The five acts (rather than the usual four), conducted with joyful vigor by Romain Dumas, fly by, and an ensemble of dancers and acrobats make a welcome contemporary addition to the proceedings.Yet “La Vie Parisienne” and “Cole Porter in Paris” both feel like extensions of a similar script. Paris, we are told, is synonymous with sexual freedom. Porter’s homosexuality and his relationship with the Russian poet Boris Kochno are strong features of “Cole Porter in Paris,” while the newly revived fifth act of “La Vie Parisienne” waxes lyrical about its setting, a cafe known for providing very discreet salons for its clients.It’s an appealing myth, which has left many in France unwilling to examine to whom, and how, that freedom actually applied. It was largely limited to a small, well-to-do subset of the population. And if Paris is the city of hedonistic romance, the argument goes, why regulate office affairs or tamp down on harassment today? “Trying to steal a kiss, or speaking about ‘intimate’ things at a work dinner” — isn’t it part of French culture, as Catherine Deneuve and others implied in an open letter in the wake of the #MeToo movement?The ensemble in “Chance!,” written and directed by Hervé Devolder, at the Théâtre La Bruyère.LOTThe allure of a bourgeois office affair is also irresistible in homegrown French musicals in which Paris is just an incidental backdrop, like the witty and unassuming “Chance!” Written and directed by Hervé Devolder, and currently installed at the small Théâtre La Bruyère, this romantic comedy featuring three heterosexual couples and set in a Paris law firm has proved a long-running success, with over 1,300 performances at venues around the city since its premiere in 2001.“Chance!” contains multiple references to American musicals, but its attitude to workplace romances is decidedly French. Not only are these encouraged, but when the boss says he may have committed sexual harassment by propositioning one of his employees, the idea is swiftly dismissed: That’s impossible, the characters decide, since she loves him back.In “Emily in Paris,” the situation would be treated as a French quirk, providing viewers with an exotic frisson. But what are real-life Parisians to do with this idealized Paris? Take a hard look at it, for starters.Cole Porter in Paris. Directed by Christophe Mirambeau. Théâtre du Châtelet.La Vie Parisienne. Directed by Christian Lacroix. Théâtre des Champs-Élysées, through Jan. 9.Chance! Directed by Hervé Devolder. Théâtre La Bruyère, through Jan. 15. More