Fosun bid €24.60 per share for Club Med, which values the iconic holiday brand at €939 million and trumps a previous bid from Italian businessman Andrea Bonomi's Global Resorts. Bonomi's offer valued the group at €915 million.
The Italian will now have an opportunity to raise his offer, further dragging out the process, which has already lasted more than 18 months, the longest takeover battle ever on the Paris stock market. Fosun had made its latest offer just ahead of a deadline at Friday's market close.
Club Med first became a top name in the European tourism industry for its all-inclusive budget family villages.
It has since moved up-market, weathering financial storms in the process, and is now looking for further expansion, including in China where it has been a partner with Fosun.
According to company figures released earlier this month, of the 25,000 new clients Club Med attracted in 2013, 80 percent were Chinese - and the rest were Brazilians.
Fosun's new offer aims at expanding in China and Brazil but also stressed that "the group would continue to invest in France, Club Med's leading market, to continue to win new parts of the market and outperform its competitors."