Hollande met some of the 2,000 troops stationed in the CAR and held talks with the country's Interim President Catherine Samba Panza.
Arriving in the CAR on Friday after a two-day visit to Nigeria, Hollande toured the capital in an attempt to show that life is returning to normal there.
"Significant progress" has been made in the three months since the French Sangaris operation began, he claimed.
Then he announced that French troops will be going to other parts of the country, especially the west and the road to Cameroon, to try to restore calm and end sectarian violence there.
"We also have, with President Samba Panza, the objective of restoring the authority of the state," he told French soldiers. " 'What state?' you might say, 'It doesn’t exist any more' and that has been the case, not for months but for years. This explains the violence you may have encountered when coming into contact with people. We must also allow the state to recover and have the means, including financial, to fulfil its mission."
Refugees who have fled to Chad, Cameron and the Democratic Republic of Congo should be brought back, he added.
Officials travelling with him said that half of the French troops would be deployed outside the capital.
There will be 9,000 soldiers from French, European and African forces in the CAR by the end of March, Hollande said.
Hollande also met Christian and Muslim religious leaders.