The Sun says Traore, 17, was allegedly caught with the weapon outside a turnstile at White Hart Lane.
Stewards are said to have seen him acting suspiciously and asked him to turn out his pockets.
Police were called and both men were arrested on suspicion of possessing an offensive weapon.
They were taken into custody for questioning and Traore was given a formal warning.
A club insider said: "Armand had no idea he'd done anything wrong because the laws are different in France."
An Arsenal spokesman said: "He has apologised."