I think this is the first thread I've ever read where someone is insisting on staying in a rough shitty area to guarantee access to a very average school. 
I think people are being a bit harsh on the mum, she's not demanding he buys her a house exactly where she wants it. What is happening here is that the OP would like them to set up home together and be a family, and wants to buy a new house for the three of them. Great. His girlfriend wants this too, except that she wants to maintain stability and a sense of familiarity for her DD and doesn't want to take risks by ripping her out of her comfort zone and making everything all about the new man.
I totally get this and I wish more lone parents would think like her instead of bending to the demands and whims of whichever bloke is flavour of the month, to the detriment of the children's wellbeing. Especially as the relationship is still quite new - what if it doesn't work out and the girlfriend and the DD are stuck somewhere rural or foreign where they have no support network?
jock you are assuming that the daughter is controlling all of this, but perhaps it's not like that at all - perhaps your girlfriend has some reservations about being railroaded into something she's not sure about yet herself. Perhaps her stance is 'Yes, I will move in with you if you decide to buy a house very near to where I live now, but not otherwise. I'm not prepared to uproot DD and we both like it here. Take it or leave it.'
What's so wrong with that? 
If she's always been a single mum working shifts she probably needs to know that whatever happens between the two of you, she can fall back on her old routine, her friends and neighbours and her local support network. It sounds like she is happy with the prospective new school, not just her DD, and that she quite likes her life how it is. I think she wants to hedge her bets by agreeing to slot you into her existing life without having to change much else, but that is her prerogative and i can't say I blame her at this stage. If you've struggled to keep it all together as a single mum for so long, you don't just give up that independence and any element of control over your own future on a whim - or at least you shouldn't, if you have any sense.
I don't think you have children of your own by the sounds of things so maybe you can't really understand how important it is that she wants to do what makes her child happy. It's not about indulging her, it's about recognising that just because you have the power to play God with your child's life to suit your own whims, doesn't mean you always should. Just because 'on paper' you can see how moving away would be a 'better life' for her DD, doesn't change the fact that the DD won't see it that way, and her mother knows that.
Of course if a child's parents are together and they choose to relocate or choose a different school then that has to be their prerogative, but the child still has the stability and the familiarity of the family unit being a constant, without the added risks of a new relationship and a new step-parent, so it's less bad iyswim.
I think you probably should not place too much importance on France right now. It may never happen, and if your girlfriend is objecting to moving to another town or village I doubt she'll be up for moving abroad so if the job offer does come up you might be having to choose between it and her anyway.
It sounds like you are getting a bit carried away with a fairytale vision of how you want your life to be together. You seem to see yourself as her knight in shining armour and I get the impression that you feel she should be so grateful to be 'rescued' and taken care of that she should be happy to just hand over the reins to you to make all the decisions going forward.
I think you should slow down a bit and not put pressure on one another either way. I certainly don't think you should buy a house in an area you are not happy with., that would be madness, unless you genuinely think it would be a good financial investment to be sold or rented out later - and that may well be the case.
Why don't you look for a compromise by buying a house in a nicer area within reasonable commuting distance of the school, let her stay in a rented place within catchment of the school until the place is secure, and then they can move in with you and commute?
Or if no compromise on area can be found that is near enough to the school, you buy a house where you want to live, maybe rent it out and live with her in the short term, or just visit them a few times a week? Then take a view on it in a year or two. By that stage if the France thing becomes a reality then it will be make or break time for the relationship anyway. She'll either feel comfortable/committed enough to agree to go with you, or she won't, but at least if you break up you won't be stuck with house in a place you hate.