Club Med, which operates around 70 resorts, said it would appoint a committee of independent directors to assess the offer, which is expected to be filed in the next few days.
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The bid comes as travel firms and airlines across Europe have seen bookings fall in recent months.
Club Med said on Monday operating income at its holiday villages in the first-half ended April 30 fell 6.4 percent.
Bookings in Europe over the last eight weeks were down 4.6 percent, mostly due to a weak French market, while they jumped 13.9 percent in Asia. Net debt at the end of April stood at 112 million euros, down from 123 million a year ago.
Club Med competes with global hoteliers Intercontinental (IHG.L) and Accor (ACCP.PA), as well as tour operators TUI Travel (TT.L) and Thomas Cook (TCG.L).
The move does not necessarily signal a new wave of takeovers in the sector, according to Christian Jimenez, who heads the Diamant Bleu Gestion fund.
This is "a very specific takeover," he said. "Fosun was already in the capital and intended to raise its stake and Club Med's management backs the deal."
AXA Private Equity holds 9.4 percent of Club Med, while Fosun owns 9.96 percent.
Giscard d'Estaing, who became CEO in 2002 and who is the son of former French President Valery Giscard d'Estaing, is also taking part in the deal. He currently owns less than 0.01 percent of the share capital. He will remain CEO if the takeover goes ahead, with Michel Wolfovski remaining deputy CEO.
Control of Club Med will be exercised through a joint venture that will be 46 percent owned by Fosun, 46 percent by Axa Private Equity, and 8 percent by 400 Club Med managers.
Should the buyers secure 95 percent of Club Med, they reserve the right to squeeze out other shareholders.
Dominique Gaillard, managing director of Axa Private Equity, said that after four years, shares may also be listed in Hong Kong.
($1 = 0.7734 euros)