Road bike for a 10 day trip in the Pyrenees and French rivera and other questions
With no training in the mountains it'll be quite painful I suspect regardless of what bike you have.

If it were me I'd just take my road bike with panniers containing a bit of food etc. My Trek 1.5 2011 cost between 500-700 quid and is, in my limited opinion a fantastic bike. 

I can't say that's the best solution, but I'd confidently take my trek up those mountains. Might be worth getting with a triple chain ring (3 cogs at the front) otherwise you might really struggle if you've done no training.

Saddle wise you stick with what it comes with and get some decent cycling shorts. Remember to keep back some money for:


Helmet
Cycling shoes/pedals perhaps?
Cycling sunglasses (think rims/easier for seeing)
Lock
Tools including cleaning stuff, pump, spare tubes etc.
Lights
Other things I haven't mentioned.


Good luck!! And get training, that'll make the biggest difference!