I think the smile was obviously fake. Cloud seemed to be looking for a way to end the conversation. The short silence seems to be him trying to say to himself "Yeah, that's right. Aerith IS GONE. I'm just deluding myself." Then he smiles so he doesn't have to say anything else. Then later he leaves for Aerith's church. (or just leaves)
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I think Cloud's fake smile was one of reassurance.
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It does seem like all Cloud wanted to do was end the conversation. He just found out that his hope of Aerith bringing him this little boy was literally just shat on. And he really needed to know that it was Aerith who led Denzel to him, and Tifa told him he was wrong. That had to have sucked to be in that situation.
I got an awkward feeling from that silence and the wording "...finally smiled" because, that does come off forced or fake.
And if it was supposed to be all mushy I think the writer should have put more to the sentence instead of just saying he stared at her then finally smiled.
But they didn't. It was just empty--like his smile.