PARIS (AP) — The most coveted accessory at the Paris Fashion Week shows this week was not a bag, a sneaker or a watch. It was an ice pack.

As a historic heat wave gripped the French capital, fashion houses fought to keep guests cool with mist machines, chilled towels, parasols and iced Evian on silver platters.

It wasn't enough. Historic venues sweltered, guests were packed in tight, air conditioning was absent or inadequate and water ran short — at one house, organizers weighed serving none at all, having found only plastic bottles to hand out.

That mattered because Paris Fashion Week is not a minor cultural event.

It is one of France's most visible export machines: six fashion seasons a year, global luxury houses, celebrities, editors, buyers and clients moving through an industry worth billions, often inside aging venues built for a cooler age.

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This week raised a harder question: whether Paris should keep staging menswear and haute couture in the height of summer at all if climate change keeps bringing more frequent and intense heat waves.

"I honestly thought I was going to pass out," said Ben Freeman, a London-based fashion critic from Australia.

Paris neared 41 degrees Celsius (106 Fahrenheit) during a heat wave that pushed France into emergency mode. Large parts of the country were under red alert, and hospitals were told to prepare for more heat-related cases.

Like the dusty Louvre, which cut hours and said its historic building "remains vulnerable and is not sufficiently adapted to climate change," fashion week exposed a Paris problem as much as a fashion one: how to keep prestige institutions running when the weather no longer fits the building, the calendar or the crowd.

"Paris Fashion Week is the canary in the mine," Freeman said.

The deeper contradiction was on the runway.

At a Paris Fashion Week Men's where the industry paid to imagine next summer could barely survive this one, houses cooled the people watching the shows, then dressed their models in unseasonable leather, neoprene, wool and fur.

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"The calendar does not make any sense," acknowledged Dior's Jonathan Anderson, blaming fractured delivery cycles and a business that bears no relation to the season outside.

Some in the front row suggested that fashion week in the hottest months be scrapped.

"In Paris we don't have AC everywhere, it's quite rare," said Thomas Levy, 24, a fashion student outside one show. "I don't know how the models did it this week in some of the leather and knit coats."

The venues couldn't cope

Pascal Morand, who heads France's fashion federation, said organizers were following the government's heat-wave plan.

"We are conscious of the challenges and very attentive to preserving the Fashion Week experience in this context of structural change," he told The Associated Press.

The cause ran deeper — an industry whose fixed parts, from the buildings to the clothes, were designed for a cooler world and a customer who lives somewhere else.

The response included earlier shows, more water, more mist, more shade.

Fashion had already been warned about heat management. In March, Celine built an okoumé-wood pavilion in the courtyard of the Institut de France for a winter show, packed guests inside and still saw some leave because of the temperature.

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Dior shifted its show to 9 a.m. from mid-afternoon, and Rick Owens moved his forward too. Yet inside Dior's half-renovated mansion, water was scarce, there was no air conditioning, and some guests looked ready pass out.

The strain had already shown at Milan Fashion Week last week. At Thom Browne's first show there, giant misting fans ran and black umbrellas went out as guests waited out the midday sun.

Runways out of season

The clothes were made not for summer in Paris but for global markets and customers who pass the hottest months in refrigerated air — the malls of the Gulf, the towers of New York and Shanghai. For them, a wool coat in June is not a contradiction. It is just a purchase.

Louis Vuitton presented wetsuits in neoprene, as well as coats in cashmere and fur.

At Saint Laurent, Anthony Vaccarello sent models through cooling clouds of vapor from a Fujiko Nakaya fog sculpture, then ran hot and cold at once: featherweight, unlined tailoring stripped down for the heat, against leather briefs, choker scarves and transparent shoes fogging with the wearer's sweat.

Issey Miyake's IM Men gave the clearest practical answer, handing out ice packs at the door, then bamboo-thread fabrics and shadowy prints that moved with the air rather than against it.

Rick Owens made the anxiety literal, sending models through mist in garments with fans whirring inside. One critic called it metaphor for climate catastrophe.

France's uneasy cooling debate

Air conditioning remains culturally suspect in France — blamed for sore throats, dismissed as wasteful or bad for the planet — even as heat waves turn cooling into a question of public safety.

READ MORE: France restricts public drinking and outdoor sports as heat wave bakes parts of Europe

President Emmanuel Macron's government leans toward shade, insulation and trees; environmentalists warn that mass cooling would only deepen the emissions driving the heat.

Europe is the fastest-warming continent, but its old cities are short on the cooling a hotter climate demands. From sport to tourism to construction, industries built around fixed calendars and outdoor crowds are being forced to adapt to heat that comes earlier, lasts longer and climbs higher.

The question is how much longer an aging 19th century Paris can host a summer spectacle where guests need ice packs to reach the finale.

Colleen Barry in Milan contributed to this report.