For nearly four years, the Tiffany & Company flagship store on the corner of Fifth Avenue and East 57th Street was shrouded in scaffolding while it underwent a full-bore renovation. In the days before the reopening, set for April 28, a Tiffany executive vice president, Alexandre Arnault, and the company’s chief executive, Anthony Ledru, monitored final preparations as they whispered to each other in French.

Display cases glittered with Tiffany pieces — heart tag bracelets, Elsa Peretti Bone cuffs and Paloma Picasso necklaces. Digital screens encircling the room showed an animation of a diamond-encrusted bird fluttering across the New York City skyline.

“We asked ourselves lots of questions going into this,” Mr. Ledru, 50, said. “Are we going to change the feel? Do we respect tradition? We decided to do both.”

He gestured toward the digitized bird, noting that it was based on a design by the noted Tiffany jewelry artist Jean Schlumberger.

“There’s that tension: modernity and heritage,” he said.

A lot has changed at Tiffany since the makeover began. Namely, the company’s ownership. In 2021, after fraught negotiations, LVMH Moët Hennessy Louis Vuitton acquired Tiffany for about $16 billion. The sale was one of the largest deals ever in the luxury world, as well as LVMH’s most significant American brand acquisition to date.

In effect, the jewelry emporium became the property of Bernard Arnault, the 74-year-old founder, chairman and largest shareholder of LVMH, who recently dethroned Elon Musk as the world’s richest person, according to the Bloomberg Billionaires Index. Over three decades, he has built a kingdom of more than 75 brands, including Dior, Celine, TAG Heuer, Bulgari, Fendi, Dom Pérignon and Sephora.

As construction workers toiled away on the ground floor last week, one of Mr. Arnault’s five children, Alexandre Arnault, 30, stood near the spot where “Equals Pi,” a painting by Jean-Michel Basquiat, would go. The painting, which features a shade of blue similar to Tiffany’s signature color, appeared prominently in Tiffany’s 2021 “About Love” ad campaign starring Jay-Z and Beyoncé.

“When people enter from Fifth Avenue, they will see the Basquiat,” said Alexandre Arnault, who wore a Dior suit and Loro Piana sneakers. “It’s an important part of the Tiffany brand now.”

Tall and lanky, Mr. Arnault, who is responsible for much of Tiffany’s creative vision, was one of the architects of the “About Love” campaign. The use of the Basquiat spurred a bit of controversy when a former Basquiat assistant insisted that the artist hadn’t intended any homage to the brand.

But that didn’t matter much from a marketing perspective: The Tiffany name was in the news for days, signaling that it no longer belonged solely to the era when Holly Golightly (portrayed by Audrey Hepburn) admired the vitrines of its flagship in the 1961 film “Breakfast at Tiffany’s.” The new Tiffany, the LVMH Tiffany, was showing itself as a brand that could also be disruptive and viral.

Amid speculation about which of the Arnault children will succeed the LVMH founder, Alexandre Arnault was tasked with the job of overseeing the renovation of the Tiffany store, which the company calls the Landmark. Before moving from Paris to New York two years ago to immerse himself in the project, he reinvigorated the luggage company Rimowa, another LVMH brand, through collaborations with Virgil Abloh and Supreme.

Mr. Ledru, the Tiffany chief executive, who was born in the Brittany area of France and raised in Lille, is a luxury industry veteran who has worked for ​​Louis Vuitton, Harry Winston and Cartier. When a droplet of blood appeared on his chin that afternoon, the result of a shaving cut, a publicist hurried to fetch him a napkin.

“This is not just another flagship,” Mr. Ledru said. “For us, the Landmark is now the lighthouse of the brand.”

The reboot left the building’s facade untouched, and the Atlas statue clock still sits above its entrance, but it spared little else. The Landmark unabashedly represents LVMH’s desire to imprint its DNA onto the company founded in 1837 by Charles Lewis Tiffany and John B. Young.

The Tiffany flagship opened on Fifth Avenue in 1940. When the gut renovation began in 2019, the store moved into the former Niketown site next door. The Landmark was designed by the architect Peter Marino, and its 10 floors are replete with works by artists like Damien Hirst, Jenny Holzer, ​Richard Prince and Rashid Johnson. Flashy accouterments include a Daniel Boulud restaurant, the Blue Box Cafe, which serves a “Breakfast at Tiffany” meal, and an Audrey Hepburn experience room that features a replica of her black Givenchy dress from the movie’s opening scene. (LVMH acquired Givenchy in 1988.)

“People relate a lot to her when it comes to Tiffany,” Mr. Arnault said. “So we wanted to make a homage to her.”

While giving a tour of the building to a reporter, the two executives walked up an undulating mirror-lined staircase inspired by Ms. Peretti’s designs. The third floor specialized in wedding and engagement rings, the fourth in gold and diamonds, the fifth in silver and the sixth in home goods and accessories. The seventh floor included a Patek Philippe department and a jewelry workshop.

Mr. Ledru described the nuances that went into designing each floor, while Mr. Arnault strayed from the press tour, inspecting side rooms and taking photos with his phone.

Earlier, the two executives had sat for a more formal interview on a green couch in a book-lined room. Conservative and tight-lipped in its approach to public relations, LVMH would not disclose the Landmark’s construction cost. A publicist, who sat in on the interview, said beforehand that inquiries about the LVMH succession were off-limits. Nonetheless, Mr. Arnault and Mr. Ledru fielded a few hot-seat questions.

At age 30, was Mr. Arnault feeling any heat to deliver on his mission for the family?

“Am I sweating?” he said. “No. Because I’m surrounded by the best professionals we could have.”

On the eve of the Landmark’s opening, were they concerned about talk that a recession may be on its way?

“There’s ups and downs, but the one thing about the U.S. is that it comes back strong,” Mr. Ledru said. “New York is much stronger now than it was last year and the year before. I don’t want to be overly confident, but we’re happy to finally open our doors.

Mr. Arnault added: “We’re releasing our Q1 numbers for LVMH tomorrow. I encourage you to have a look.”

(The day after the interview, LVMH reported a 17 percent rise in first-quarter sales, surpassing analyst expectations. In response, French workers protesting against pension changes stormed LVMH’s Paris headquarters, calling for the rich to contribute more financing to the state pension.)

If they weren’t nervous about the economy, were they worried about anything else?

“I’m anxious for the first holiday season,” Mr. Arnault said. “It’s such an important part of American culture. This is the first one back at the original Tiffany’s corner.”

“We were a lot more anxious a year ago, when we were receiving phone calls from Mr. Arnault asking, ‘When do you open?’” Mr. Ledru said.

After the two men finished their tour of the Landmark, they stepped onto the building’s eighth floor deck. They stood in the fresh spring breeze as they took in the view of Fifth Avenue.

“Pas mal, non?” Mr. Ledru said. (“Not bad, no?”)

While construction workers hammered away behind them, hurrying to add the final touches on a glass-walled event space, Mr. Arnault took note of several other LVMH properties within his sight: There was Louis Vuitton just across the street, Bulgari opposite it and Dior down the way.

He smiled.

“I can spy on them,” Mr. Arnault said. “I can make sure they’re working from here.”