"The corpse of (Camille) Lepage was found after a patrol by (French) Sangaris troops stopped a car driven by anti-balaka groups, in the Bouar region," Xinhua quoted Hollande as saying in a statement.
"Everything will be done to know the circumstances of this assassination and to track down who murdered our compatriot," it added.
The 26-year-old freelance photo journalist had been based in South Sudan since July 2012.
On May 6, Camille Lepage said on social media that she was travelling with anti-balaka fighters to Amada Gaza in western Central African Republic near the border with Cameroon.
Since the start of Sangaris operation in December 2013, three French servicemen were killed in the poorest African country that was hit by a long political unrest.
Media reports said there has been an escalation in fighting recently as mainly Christian militias, known as the anti-Balaka (meaning anti-machete) movement, are now targeting Muslim communities in the CAR capital of Bangui, and in the west of the country.
A total of 2, 000 French soldiers have been deployed in CAR so far to help restore order.