The two spoke privately for 35 minutes with the assistance of an interpreter from the Vatican Secretariat of State, although before and after their private talk, the pope spoke to Hollande in French.
Media attention to the visit was high, particularly given recent revelations about Hollande's affair with an actress and its impact on his official companion, to whom he is not married.
Security was tight around the Vatican for the visit after a rudimentary bomb exploded in Rome the night before near a French chapel, damaging several cars parked on the street and breaking the windows of some buildings.
Passionist Father Ciro Benedettini, a Vatican spokesman, confirmed reports that an anonymous call to Rome police at 9:30 the morning of Hollande's visit claimed that two bombs had been placed under the colonnade surrounding St. Peter's Square.
As is normal when a head of state is about to visit, a thorough security check of the area already had been performed, Father Benedettini said, but the colonnade was checked again. It was a false alarm.
Before the visit, Hollande's press office issued a statement saying he planned to discuss with Pope Francis their shared concerns about the Middle East, Syria and the Geneva II peace talks and the ongoing conflict in the Central African Republic.
"The meeting will reaffirm his commitment to regular and trusting relationships between the government and the Catholic Church," the press statement said.
The Catholic Church and Hollande's government have experienced tensions since the president's election in 2012, particularly concerning Hollande's support for the legalization of same-sex marriage. In May 2013, he signed a law allowing gays and lesbians to marry and to adopt children.
Current debates in France about legalizing surrogate motherhood and broadening access to artificial insemination and in vitro fertilization also have drawn the criticism of French bishops.
Writing in the Catholic daily La Croix Jan. 23, Cardinal Philippe Barbarin of Lyon said the proposed laws, which would be designed to make it easier for single people and gay couples to have children, would change what it means to be someone's child. "For the first time, a generation of children will be born who have intentionally been deprived of one of their parents."
The provisions would place the desire of an adult to have a child above the rights of a child to know who his or her parents are, the cardinal said. Placing the rights of the strongest over the rights of the weakest already occurs with "the law on abortion, which began as an exception to respond to situations of serious difficulty, but has transformed quickly in recent decades."
A Vatican statement about Hollande's meeting with Pope Francis and later with Cardinal-designate Pietro Parolin, Vatican secretary of state, said that "in the context of the defense and promotion of the dignity of the human person, several topics of current interest were discussed, including the family, bioethics, respect for religious communities and the safeguarding of places of worship."
Poverty, development, migration and protecting the environment were also discussed, the Vatican said. And Hollande told reporters later that Pope Francis had said he was preparing a document on the environment.
As a member of his official delegation, Hollande brought with him Father Georges Vandenbeusch, a French missionary in Cameroon who had spent seven weeks as a hostage of the Nigerian Islamic terrorist group Boko Haram before being released on New Year's Eve.
"I am very happy," Pope Francis told Father Vandenbeusch before reaching out to give him a big hug.
For Pope Francis and Francois Hollande, the Francis connections were strong during the meeting Jan. 24, the feast of St. Francis de Sales. As a gift for the pope, Hollande brought a copy of a 1921 illustrated edition of a life of St. Francis of Assisi.
Unlike his predecessor, Nicolas Sarkozy, Hollande's visit was not scheduled to include a visit to the Basilica of St. John Lateran, the Rome diocesan cathedral with which the French nation has a special tie. Since early in the 17th century, the French kings and several of nation's presidents have been welcomed as the "honorary canon" of the basilica.