The Major Image spell description says:
You create the image of an object, a creature, or some other visible phenomenon that is no larger than a 20-foot cube. The image appears at a spot that you can see within range and lasts for the duration. It seems completely real, including sounds, smells, and temperature appropriate to the thing depicted. You can’t create sufficient heat or cold to cause damage, a sound loud enough to deal thunder damage or deafen a creature, or a smell that might sicken a creature (like a troglodyte’s stench).
Physical interaction with the image reveals it to be an illusion, because things can pass through it. A creature that uses its action to examine the image can determine that it is an illusion with a successful Intelligence (Investigation) check against your spell save DC. If a creature discerns the illusion for what it is, the creature can see through the image, and its other sensory qualities become faint to the creature.
One of my players wants to cast this as a Wall of Fire. He asked me what would happen if an enemy shoots through it.
As noted in the bolded sentence, physical interaction with the image reveals it to be an illusion.
Arrows have no problem with getting through a normal Wall of Fire. Would this reveal the illusion?