As is, it doesn’t mean what you think, since les entrailles means literally the guts. If you want a translation, I have several propositions:

• try could be rendered as essaie, tente or vise à
• capture as appréhender, restituer, retranscrire or simply capturer
• the inside as les profondeurs or les tréfonds
• the human soul as l’esprit humain, l’âme humaine

I would go for

Le naturalisme vise à appréhender les profondeurs de l’âme humaine.

Sticking to your description “réalisme is trying to capture and describe the story that is happening inside the characters, rather than the actual events”, I would suggest the following:

Le Réalisme s’attache à restituer la psyché des personnages.

Now, if you really think of this as “capturing the inside of human soul”, you might consider something less prosaic. Maybe the following:

Le Réalisme entend reproduire les dimensions intérieures de l’être.

« Spleen » ça se peut ?

Le beau est toujours bizarre.
— Baudelaire

Sinon, je dirais

Le naturalisme tente d’expliquer l’âme de l’être humaine.