Catherine Deneuve has long been a French national treasure, and in a new movie, “The President’s Wife,” the icon plays a woman of similar status: the former first lady of France, Bernadette Chirac. Like her late husband Jacques, Madame Chirac was a conservative, and though Ms. Deneuve hints in press notes that she did not share her political views, the performer did diverge from liberal orthodoxy when she questioned the methods and reasoning behind the #MeToo movement in 2018. 

An independent thinker as well as a great actress, she complicates the claim made in the film that all artists are left-wing, even though it makes for a droll moment in a movie filled with them.

Loosely based on Mrs. Chirac’s life during her husband’s presidency between 1995 and 2007, the film works as a gentle, almost slack satire. Major events from the first lady’s tenure are mixed in with private incidents, with specious amusement the primary tone — overriding historical and psychosocial accuracy. One need not know much about French politics to enjoy its humorous take on a wife emerging from her important husband’s shadow, yet it could certainly help as there might have been some jokes, verbal or visual, that got lost in translation or presentation.

Ms. Deneuve is the main reason to see “The President’s Wife,” with the 81-year-old actress giving a wonderfully wry performance, akin to her role as a housewife-turned-boss in 2010’s “Potiche.” Leveraging her trademark cool demeanor — her very French sangfroid — and adding flourishes of displeasure, tenacity, and snobbery, she creates a character that may not be as tough or brittle as the real Bernadette has been described, yet retains the matron’s formidable intelligence, dignified bearing, and air of nobility. Director Léa Domenach has discussed how Mme. Chirac was often funny, leading her and her co-writer, Clémence Dargent, to accentuate the comedic aspect by drawing on a number of short phrases and anecdotes.

Ms. Domenach also adds absurdist elements, such as a choir that occasionally pops in to sing lyrics detailing Bernadette’s life or the Habanera aria from the opera “Carmen,” though the first-time filmmaker attempts to justify this element by aligning it with the real-life personage’s Catholicism. 

The chorus is right there at the start, on the eve of the 1995 presidential election as Bernadette goes to confession. Unusually, the sycophantic priest doesn’t recommend any prayers or attempt to temper her intuition of victory within a broader spiritual context, instead praising her talent for “analyzing situations.” This phrase and other too-on-the-nose assessments early in the film bring us up to speed on her persona even as they come off as strained.

Once Bernadette is installed at the official residence of the French president, the Élysée Palace, the real fun begins. Despite strongly supporting her husband in public and private, and her own political acumen (the first lady was also a councillor of the French region Corrèze), she grows frustrated at being sidelined by him and his advisors, including their daughter Claude (Sara Giraudeau). 

Her tendency to express this dissatisfaction openly leads to her being assigned a meek public relations advisor, Bernard (Denis Podalydès). Yet when Chirac’s affair with an Italian actress (possibly Claudia Cardinale) is revealed, she decides to revert back to her more uncensored personality. Additionally, the sometimes sour and aloof Bernadette undergoes a modernizing transformation meant to boost her likeability, complete with an updated Chanel wardrobe and a lightly feminist outlook. 

While Michel Vuillermoz is both entertainingly dunderheaded and believably sexist as “Super Liar” Jacques Chirac, it is Bernadette’s relationship with Bernard that provides the film with its core relationship. The chemistry between Ms. Deneuve and Mr. Podalydès, with his inept functionary face and her arch poker face, twinkles with mirth. 

At times cleverly staged, the comedy also features awkward shots, messy editing, and a diffuse structure. Plus, there are far too many moments in which characters turn off TVs and radios when the news disappoints them — why not change the channel or station instead? Otherwise, archival news items are put to good use, with the filmmakers even adding Ms. Deneuve into footage of Hillary Clinton visiting Corrèze with Mme. Chirac.   

During the final stretch in the early-to-mid-aughts, scenes related to President Chirac’s eventual successor, Nicolas Sarkozy (Laurent Stocker), continue the playful spirit even as the film submits a bit to the staid biopic approach after the French patriarch suffers a minor stroke and Bernard moves on to another position. The disclosure of her other daughter’s anorexia also presents the dark side of her image rehabilitation campaign. 

One naturalistic scene, in particular, surprises: Bernadette, in conversation with Claude, suggests that she may have weathered her husband’s philandering, condescension, and dismissiveness in order to keep the family together. The grande dame chalks it up to being a traditionalist and behind the times, with her daughter replying, “Thanks for being old-fashioned.” It’s a lovely, sincerely delivered sentiment in a movie that affects a pleasantly mocking tone but never becomes fashionably biting in its examination of politics and marriage.