Again: SPOILERS ahead!

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There's clearly some uncertainty about whether the very last scene of the last episode means Francesca stayed, or if it's just a flashback to the episode before, when they were snowed in.

Unless the producers are extremely sloppy with continuity:

She stayed. :-)

The earlier night where she had to sleep over because of the blizzard, she was wearing the huge white buttoned shirt that Arnold left behind -- you might remember the scene where they talk about it -- but in the last scene of the finale, she is wearing a dark, short-sleeved t-shirt of some kind. So I'd say it's pretty clear she stayed.

(Normally I'd say that makes me happy, but I'm fairly confident that they're gonna make sure things doesn't continue/end well when the next season comes. This kind of show, brilliant as it otherwise is, seems to think things can't possibly go well for the protagonist in the end without it turning too mainstream and commercial. But here's to hoping they get smarter on that issue...)