France, June 26 -- 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, organisers 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.

This...