Barclays is selling off 74 French branches
The network has 74 branches across France, offering current accounts, mortgages and wealth management products.
Barclays will keep its corporate and investment bank activities.
Anacap has more than €3 billion (£2.2 billion) under management and invests primarily in financial services businesses.
Other banks in the Anacap stable include Aldermore in the UK, MeDirect in Belgium, Mediterranean Bank in Malta, Equa bank in the Czech Republic; and FM Bank in Poland.
Nassim Cherchali, Director of AnaCap, said: "This is an opportunity to acquire an attractive and established banking operation built on a team of highly talented individuals with exceptional relationships with customers across France."
"We have already established an unrivalled track record within the private equity industry for acquiring and growing banking platforms across the continent and, if concluded, we look forward to building this business further in a market with significant potential for innovation and expansion," Cherchali said.
Barclays is in the process of selling off non-core assets, including its Africa division.