What to do with the PPL
Nick, the most important thing to do with your new PPL is enjoy yourself. The license is a ticket to a whole world of experiences that the average ground based mortal will never understand. Just like a driving license the PPL is a license to learn and there are limits to what you can do with it in a practical sense.
In response to your questions:
Yes you can fly over to France once you have your license, however if you want to get to the mountains expediently (in the winter) and safely you will preferably need an aircraft which is deiced and pretty quick (140kt + cruise) with a decent service ceiling (20000ft). Having oxygen on board may also be preferable if you want to get above most of the weather (and the alps if you want the direct route to the Italian side). You would also do well to further your PPL with an IR (easiest done in the FAA system) then fly an N-registered aircraft in the airways system - much less hassle than VFR. Altiports (Courchevel etc...) are out unless you want to do special ratings so you are looking at Chambery, Grenoble and larger airports with instrument facilities and tarmac runways if you want to be able to land there in a reasonably fast aircraft in the winter. There will also be plenty of weather that is just too harsh to risk getting in to (even with your airways equiped deiced A/C and your IR) and making this judgement call comes with experience.
You are absolutely correct in realising that off airport transport is a pain. Little airports tend to be in the middle of nowhere with non-existent transport links so if you can carry some wheels with you then you can continue your journey unbroken (albeit at about a tenth of the speed!) The diblasi folding moped works well for me (I have a couple that I carry in the back if needs be - fastest light-a/c-portable road legal transport IMHO) - you can also get a folding bicycle in (although I guarantee you will look a huge nerd astride anything you can carry in the back of your plane). I always have my driving license with me and will often rent a car at the destination rather than risk the Spanish equivalent of the M1 on my 49cc put-put.
Think IR rather than plain PPL if you really want to ski.
I'm off to the Italian alps on Thursday, not taking my moped though - too bloody cold!
My advice - do the FAA PPL then if you like it add an IR and if you become an addict (like so many of us on this site) buy an N-registered aircraft and use it as much as possible.
Good luck,
SB