The UK bank said the businesses being sold comprise a network of 244 retail branches, which serve 800,000 customers, and had assets of €7.1bn.
Noel Quinn, HSBC’s chief executive added: "The signing of an MOU for the potential sale of our French retail banking business represents a significant step in progressing the actions we announced during our strategic update earlier this year.
“It will enable us to dramatically simplify our business in Continental Europe and allow us to accelerate the transformation of our European wholesale banking franchise.
“We are committed to remaining as a leading international wholesale bank in Continental Europe, capitalising on our global network and serving our multinational customers both inbound and outbound."
HSBC has been exiting its retail banking operations outside its core areas of Asia and the UK.
Last month, the bank confirmed it was pulling out of US retail banking after initially entering the market in the 1980s and said its retail strategy going forward would be to focus on high net worths and businesses in Asia.
HSBC added it expected to complete its French disposal in the first half of 2023, with an estimated loss on the sale of US$2.3bn plus an additional US$700mln goodwill impairment.
Going forward, the European operation would “connect trade and capital flows between the west and the east, supporting delivery of our growth ambitions in the Group's distinctive Asian and Middle Eastern businesses”, it said.
Paris would remain the hub for HSBC in Continental Europe, it added.
HSBC shares shed 2% to 431p.