Fosun, whose earlier offer was estimated at €839 million, upped its offer for the iconic holiday brand to €24.60 per share to €939 million.
Fosun is competing against a bid from Italian businessman Andrea Bonomi's Global Resorts which last month upped its offer to €915 million.
The bidding war has lasted for 18 months already and is the longest recorded on the Paris stock market.
Fosun raised the stakes just ahead of a deadline timed with Friday's market close.
Bonomi now has until January 7 to respond.
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, 80 percent of the25,000 new clients Club Med attracted in 2013 were Chinese, and the rest were Brazilians.
Fosun's new offer aims at expanding in China and Brazil but also stressedthat "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."
The group is struggling however, reporting a net loss of 12 million euros thisyear, with a turnover of €1.38 billion.
It owns 70 holiday villages in 26 countries and employs some 13,000 staff.