The man was "detected upon his arrival at the hotel on the Disneyland site where he had a reservation. Hotel security found two handguns, a Koran and ammunition on him," the source said.
Disneyland Paris said the guns were picked up by routine scanning of the man's bags at the hotel entrance.
A police source said preliminary investigations did not point to terrorism, and that the man had said he was carrying the guns because he feared for his safety.
France is on high alert after November's attacks saw gunmen and suicide bombers target cafes, a concert venue and the Stade de France national stadium, leaving 130 dead and hundreds wounded.
The Islamic State group claimed responsibility for the carnage.
In Thursday's incident, police arrested the suspect and secured his vehicle.
They then arrested a woman, believing her to be his girlfriend, but released her after realising they had the wrong person, one of the police sources said.
Papers found on the suspect indicated that he lived in Paris, but no further details were given. His girlfriend is still being sought.
The scene unfolded at the Art Deco-style New York hotel near the theme park, which is situated about 30 kilometres (18 miles) east of the French capital.
"Police were immediately warned and the individual was arrested. We are continuing to work closely with the authorities and the safety of our visitors and employees is our top priority," a spokesman for Disneyland Paris, Francois Banon, said in a statement.
The suspect was the joint manager of a brasserie in Paris's 14th arrondissement, according to a source close to the investigation.
Staff and regulars said they were “astonished” by the arrest.