Use Montresor's cues to do this. In the beginning of the story, he relates that Fortunato has injured him thousands of times, but he doesn't describe a single one of them. He also says that he has never let Fortunato know that he is angry with him. So, as far as Fortunato knows, he and Montresor are very good friends. From Fortunato's point of view, the story could start at the carnival where Fortunato is drinking wine and having a good time. Since it is from his point of view, the "I" of the story will be Fortunato. He would be happy to see Montresor.
When he meets Montresor, he can not wait to show off his wine knowledge by testing the amontillado. Therefore, his inner thoughts should play on this pride. And in the style of Montresor's narration, Fortunato can relate some of his thoughts as if he is telling the story to someone else. He won't be able to do this in hindsight, years later as Montresor does because presumably, Fortunato dies entombed. Therefore, he will tell the story in the present tense. (Unless of course, you want to throw a twist in and suggest that Fortunato has escaped somehow and for years has been plotting revenge.)
But as he descends into the vaults, Fortunato dismisses Montresor's warnings about the dampness and his health. So, maybe Fortunato's inner thoughts illustrate his determination to reach the amontillado. They might also illustrate his rivalry with Luchesi as the most reputable wine connoisseur. He continues to drink as they descend further in. As storyteller, he might acknowledge this or be oblivious to how drunk he is becoming.
When Montresor starts to wall him in, this is when fears begin to surface. Perhaps, even at the latter moments, Fortunato still thinks it is a big joke. Maybe the end of the story shows Fortunato wondering what he could have done to Montresor to receive such punishment.