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.

But the objects are just some of the Mary Rose artefacts which have gone on display at Swansea University.
Researchers have been examining the artefacts from Henry VIII's warship, which was raised in 1982, to discover more about the ship's crew.
Their work has revealed that many of those who perished when the boat sank in 1545 were "superb athletes".
Sport physiologist Dr Nick Owen said the skeletons and objects raised with the Mary Rose have given them a "wealth of information".
"The abnormalities in some of the crew's radius bones shows that they'd have been supreme athletes," Dr Owen said.
"Today an Olympic bow has 48 lbs of tension, but to fire a Mary Rose bolt (arrow) would have taken well over 100 lbs."
Dr Owen believes that as well as providing a glimpse into the past, his team's discoveries can offer an insight into the injuries of modern athletes.
"You can see similar abnormalities in elite tennis and squash players," he said.
"Top sportsmen are singled out for elite training from such a young age.
"The cream of archers on the Mary Rose would have been in training since they were seven years old."
Dr Owen's team, including scientists from the University of Bradford, have already succeeded in creating an online 3D image of some of the sailors, which can be remotely studied by scientists.
The next challenge is to see what lies inside the bones.
"Once we can conduct Micro CT scans, we'll be able to see what changes being one of Henry VIII's elite archers caused internally," Dr Owen explained.
"These very fine scans will help us discover how their lifestyle and diet affected their bone structure from the inside."
The Mary Rose artefacts are on display to mark the university's research and innovation awards evening.
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".
[NEXT_CONCEPT]
A boot, some old skeletons and a block of wood might not sound like the type of thing to entice you to Swansea.