PARIS — Despite bowing to an important union demand, Air France-KLM remained crippled on Thursday by an 11-day-old pilots’ strike.

After the company said late Wednesday that it had canceled the proposed Europewide expansion of its low-cost unit Transavia, the union responded on Thursday that its representatives had “made reasonable proposals” to break the stalemate but that “management chose to refuse them.”

With hopes of a breakthrough fading, Air France cautioned that it expected to operate only 48 percent of its flights on Friday, with an estimated 58 percent of pilots planning to remain on strike.

The pilots’ strike, which has forced the airline to ground more than 6,000 flights, was touched off by Air France-KLM’s announcement this month that it planned to invest 1 billion euros, or $1.28 billion, to make its budget carrier, Transavia, better able to compete in Europe’s discount-travel market.