I think all the people on the island are in heaven, or some big group dream or something. Wherever they are they all get exactly what the really want in of life. Whether or not they like what they truly want is another story. I should point out that just because someone really deep down wants something from life, does't mean they'd be will to admit it. Sawyer is a good example, I don't think he'd ever admit that he just really likes being a jerk to people, but that is what seems to make him happy.
I'll list some of the people and give examples as to my theory. So far my theory applies for all the people on the island. The obvious one is Locke. Homeboy number one can walk now, and number two he gets to be this crazy hunter that supplies food for the island. It was obvious from his storyline that he was really into hunting and the outdoors. Jack gets to be a leader and a doctor that everyone turns to when they need help. Pretty self explanatory that he wants to be a good doctor. Mercutio gets his son back which he's always wanted but never really been able to get. Ultimately his son says he really likes his new dad, but I don't buy it. And besides what kid that grew up without their real dad doesn't secretly want to at least know them.
The asian guy gets his wife in a seriously subservient role, and his wife gets a love providing husband that's not in the mafia anymorw. This is a little iffy on the wife's side but I think it will flesh out more in the future. Charlie gets to kick drugs which he's needed to do for a long time, and maybe settle down with Claire. Boone gets to be close to his sister, and his sister gets the ultimate protection from her brother. It seems pretty obvious that Boone is way overprotective of his sister. While she may have turned his help away in the one episode I think deep down she really likes him caring for her.
Claire ultimately really doesn't want to be a mother. I have a feeling she'll come back and he baby will be gone. She may be upset about it, but I don't think it'll be too bad because it really seemed from her storyline that she didn't want to be a mother. Sawyer just gets to be a jerk because that's what he really likes, hording all the stuff and having people subjugate themselves to get it. Sayid gets to go all Gilligan's Island professor on everyone and build radios from coconuts and translate weird maps and crap.
The only one I haven't figured out yet is Hurly but I'm sure after his story is fleshed out it will make more sense. So basically the island is some sort of extension of the deepest desires of people. I think it's meant to show you that what you really want (whether you admit it or not) deep down may not really make you happy like everyone wants to believe.
As to who the french woman is, and why the polar bears I defer to the Matrix. If it's something like Heaven I think their has to be some villain, some foil to everyone getting what they really want. Sort of like the example in the Matrix, how in the Matrix version 1.0 (the garden of eden) things were too perfect and people couldn't handle it. For humans to comprehend goodness there has to be a corresponding badness.