In the end, Joe does NOT get the girl

The logical explanation is that Fran really does betray Joe. It should go without saying that just because this is what makes sense in the context of the narrative, it does not mean that it is what the writer intended. After all, Mamet's the guy who wrote a horribly contrived film called The Spanish Prisoner.

So, think about it this way: According to the folks insisting Fran and Joe ultimately end up together, we're supposed to believe she ditches Jimmy Silk some time after picking up the fake gold. Why?? She could ditch Silk before. Alternatively, she could say she doesn't know where the loot is, or she could give him a location that turns out to be false, and then ditch him whenever she damn well pleases. Instead we're supposed to believe Fran leads him to the right location, needlessly risking Joe's life and the gold for some ridiculous added twist.

No, the only explanation that makes sense is that she betrayed Joe.