On his two-day tour of communist Vietnam, Hollande hailed economic ties with the former French colony but sidestepped talking about rights issues publicly.
The four are a Catholic dissident, a blogger, a land rights defender and an activist who tried to form an opposition movement, according to the source travelling with the president.
Their names were passed to Vietnamese authorities on orders from Hollande.
The one-party state is routinely criticised for its intolerance of dissent, with regime critics regularly arrested or jailed and all newspapers and television channels government-run.
Among those currently in custody are businessman Tran Huynh Duy Thuc, who is serving 16 years on charges of trying to overthrow the state, and blogger Nguyen Huu Vinh, known by his pseudonym Anh Ba Sam, jailed for five years for posting anti-government articles online.
France and Vietnam signed a number of deals on the trip, including a $6.5 billion agreement with Airbus and three Vietnamese carriers for 40 planes.
Amnesty International called on Hollande Tuesday to make sure these deals did not overshadow rights issues.
"Human rights must not be sacrificed to trade and security deals. President Hollande must use his visit to call on the Vietnamese authorities to meet their human rights obligations under international law," Camille Blanc, chair of Amnesty International France, said in a statement.
France is one of Vietnam's leading European trading partners and the second largest aid donor to the country after Japan.