The incident happened at a soup kitchen in Montreuil, east of Paris.
The man said he was able to dodge the axe but was stabbed in the stomach, according to a prosecutors statement.
His condition is not said to be serious. France remains under a state of emergency since last November's attacks claimed by Islamist militants.
The victim told investigators the assailants shouted "Allahu Akbar", meaning "God is greatest", and called him an "infidel dog" before running away.
He is director at Restos du Coeur, a charity which gives food packages and hot meals to the needy.
According to Reuters, the investigation is being carried out by criminal police rather than anti-terrorism units.
Since the attacks by so-called Islamic State last year, France has been on high alert.
In June, a policeman and his partner were stabbed to death outside of Paris by a man who claimed allegiance to the Islamic State.
Police are investigating after a French charity worker said he was attacked with a knife and an axe by a couple who shouted "Allahu Akbar".