The Goûter Refuge — a futuristic structure that clings to a cliff at 12,516 feet — is, for many people, the final stop en route to the top of Mont Blanc, the highest mountain in Western Europe, straddling the border between France and Italy.

Every summer at least 20,000 people attempt the 15,776-foot summit. The majority spend a night in the Goûter Refuge, on the French side, which welcomes climbers from late May through September. Local officials and guides say the number is growing, and that today’s climbers are less experienced, even as warmer temperatures are increasing the risk of rockfall and transforming once-snowy ridges into treacherous sheets of ice. A small number of climbers also appear to be unwilling to respect the rules — or even pay for their accommodation.

“People would say, ‘You have to let us stay for free. We don’t have to pay because you’re a mountain hut,’” said Antoine Rattin, 46, a guide and the manager of Goûter Refuge, recalling a few encounters last summer.

In the high, wild landscape around the Refuge, turning people out for the night could mean death, so Mr. Rattin had no choice but to abide their presence — even if that meant accepting their refusal to pay the €65.80 (about $74) fee for a bed, and exceeding the hut’s official capacity of 120 people.