Her garments are worn by stars like Lee Jung-Jae of “Squid Games,” Choi Woo-Shik of “Parasite” and members of the K-pop sensation BTS. But when the South Korean fashion designer Woo Young-mi made her international debut in 2002, few people believed high-end fashion could come out of a country known for its war-torn history.

Ms. Woo, or Madame Woo, as she’s often called, is arguably one of the most successful Korean designers. She is the chief executive of the Solid Corporation, a company that controls two successful labels: Solid Homme and Wooyoungmi. She became the first Korean member of the French Federation of Fashion in 2011, and her Wooyoungmi line is now a staple at luxury retailers like Le Bon Marché, Selfridges and Ssense.

Ms. Woo has lived on and off in Paris for about 20 years, and has had front row seats to South Korea’s emergence as a cultural juggernaut. It’s a phenomenon that she has contributed to and benefited from throughout her career, she said.

Born in 1959, Ms. Woo grew up in Seoul during a time of rapid economic development that followed the end of the Korean War. “The national motto was ‘work hard and live well,’” she said. “Caring about fashion was seen as a social evil, especially for men.”

But Ms. Woo had an unconventional upbringing that gave her a natural affinity for the arts. Her mother, an art teacher, dressed her and her four siblings in unique, homemade clothes that made them stand out at school. Her father was an architect with only occasional work who socialized with American soldiers, collected rare items and invested in his appearance. Among his possessions, she recalled, were pieces of Bauhaus furniture, European fashion magazines and a long, leather coat reminiscent of one Clint Eastwood might have worn.

“At that time, 95 percent of men dressed the same,” she said. “Fathers wore suits and uniforms to their offices and factories, but my dad spent 80 percent of his passion on looking good,” she said, citing him as the reason she eventually pursued men’s wear design and is often inspired by art and architecture.

“Honestly, I felt ashamed by all of it — the way our house was decorated, the clothes I had to wear — but looking back on it now, I think my father was a very creative, very cool person,” she said.

Despite her background, she never thought of being a fashion designer because, she said, “words like ‘fashion designer’ didn’t exist in Korea then.” She failed to pass an exam for entry to law school, which she called “fate.”

To Osaka and Beyond

Ms. Woo said she had “momentary illusions of genius” throughout her fashion courses at Sungkyunkwan University, but it wasn’t until she was invited to compete at the 1983 Osaka Fashion Collection that she started to dream big.

Hyunji Nam, the lead editor of Korean content at Ssense, said that when it came fashion, Japan and South Korea were on very different playing fields at the time. “By the end of the 1980s, Japanese fashion was already becoming recognized abroad because of the work of names like Yohji Yamamoto and Issey Miyake,” she said. “But South Korea didn’t have the national power to support fashion in or outside of the country, and most designers, regardless of how talented they were, had few opportunities to show their work in or outside of Korea.”

The trip to Osaka was Ms. Woo’s first abroad, and she was intimidated, not only as a competitor but also as a Korean among a host of nations with more established fashion histories. She remembered the other countries coming in groups — coalitions of people from Europe, Hong Kong, Singapore — and she, a lone Korean. She stayed up the night before the competition, a needle trembling in her hands as she completed her minimalist take on hanbok (traditional Korean dress). She was stunned when she was awarded the prize.

“In Korea, no one cared that such a competition existed, and no one cared that a Korean was able to win, but it inspired me to think big about fashion,” she said.

Ms. Woo bounced around a few Korean fashion conglomerates before starting her first business in 1998, a small boutique in Seoul, with her younger sister, Jang-Hee. “She was the one who always told me I could do it, when I felt like I couldn’t,” Ms. Woo said about her lifelong business partner, who died in 2015.

They called the ready-to-wear men’s wear label Solid Homme and described it as clothes for their ideal man. “I imagined him to be straight and narrow, the sort of good guy most girls would want to marry,” Ms. Woo said. The results were clean-cut, minimal looks that many at the time described as metrosexual.

Ms. Woo said the label hit the market at the right time: just ahead of the 1988 Summer Olympics in Seoul. Foreign tourists and Olympics attendees were flooding the capital, and Koreans were becoming interested in how non-Koreans looked and becoming more open-minded about a diversity of styles, she said.

In particular, Solid Homme caught the eye of two groups of trendsetters. The first were called Orenji-jok (Orange tribe), a group of wealthy teenagers and 20-somethings, often from the Gangnam district in Seoul. They had traveled abroad and were interested in fashion with a Western edge.

The second were Korean music’s first ballad singers, like Lee Moon-sae, Lee Seung-Chul and Yoon Sang, who catered to mostly female audiences. Solid Homme grew via word of mouth and celebrity exposure.

“Solid Homme and Wooyoungmi have been go-to brands for male Korean celebrities for as long as I can remember,” said Gianna Hwang, a stylist for clients like Lee Jung-Jae, Eric Nam and Song Kang. “It’s not easy for a men’s wear company to achieve this kind of soft but beautiful look that both these brands possess. Her clothes are slightly oversize, as per the trend nowadays, but overall, they have an amazing fit, which is the most important thing if you’re dressing men.”

Today, with more Korean celebrities traveling overseas for fashion shoots, there is a growing conversation about adding hints of Korean style to outfits. “There are a lot of worthwhile Korean brands nowadays, but neither Solid Homme or Wooyoungmi are just Korean brands,” Ms. Hwang said. Ms. Woo, she added, is “a great designer who only happens to be Korean.”

Lessons in French Baking

Fourteen years into Solid Homme’s success, Ms. Woo said it wasn’t enough that she was doing well in Korea. She wanted to create a luxury brand for a more sophisticated and sensitive adult, unafraid to be vulnerable. And despite friends and acquaintances expressing concern, she wanted to do it in Paris, the fashion capital of the world.

“They told me I was crazy,” she said. “First, they said I couldn’t do it because I’m Korean. Then they said it’d be all the more impossible because I was a woman.”

Others suggested that if she wanted to appeal to Europeans, she should play up her label’s Korean-ness and make clothes that looked more visibly Asian. “They said it was like trying to sell croissants in Paris,” Ms. Woo said.

“If you want to make it as a Korean, you have to sell tteok,” she said, referring to Korean rice cakes. “You have to make something they don’t already have. But what could I do? I wanted to make croissants.”

The French fashion scene did indeed turn out to be uninviting to her. At Paris Fashion Week, Wooyoungmi’s show time slot was rescheduled multiple times — even after invitations had been sent — and models she had hired were scouted by other designers, she said. The collection finally debuted on a Sunday at 10:30 a.m., the morning after the biggest Fashion Week parties, to fewer than 150 guests. Were it not for one positive review in Le Figaro, she said, she might have given up altogether.

Ms. Woo vowed to become a full member of the French Federation of Fashion, believing a seat at the table was the only way to secure the label’s future at Paris Fashion Week, but the path there wasn’t easy.

Until 2009, her team operated without an office in Paris, brought everything — scissors, needles, thread — from Korea and worked out of hotel rooms. On multiple occasions, she was rejected by showrooms that wouldn’t take a chance on a Korean designer. One of the most humiliating experiences, she said, was at a meeting with a showroom in which the owners spoke over her in French — “Korea? Do you know where that is? Are Koreans doing fashion now?” — as if she could not understand.

“I held it together until the meeting was over and cried and cried afterward,” she said. “But I showed there, did well there and left on my own accord just like I promised myself I would.”

Korean Men Glow Up

In the last decade there has been a shift in how Korean fashion, and men’s fashion in particular, is talked about.

The South Korean luxury market boomed and now ranks the seventh largest in the world, according to Euromonitor, a market research firm. Sales of men’s skin-care products alone increased 44 percent between 2011 and 2017. And, of course, as Korean men invest more time and money on fashion, the world is seeing more of them.

“It’s not like one thing happened after another,” Ms. Woo said. “It’s that all these factors interacted with one another.” Then she added, “It was also me.”

Wooyoungmi now has 44 stores across Asia, Europe, North America and Australia. Ms. Woo has expanded into jewelry, accessories and women’s wear. Last year, she collaborated with Samsung on limited editions of Wearable Wooyoungmi items. According to data by Korea’s Financial Supervisory Service, the Solid Corporation earned 548 billion won ($46 million at the time) in 2020, up 20 percent from two years earlier.

“Wooyoungmi elevated the perception of Korean fashion overseas by proving it could be done,” Ms. Nam, of Ssense, said. “A Korean designer could be a regular at Paris Fashion Week. A Korean brand could be sold at luxury department stores.”

Ms. Woo, she added, “paved the way for future designers to come.”