In reply to TheFasting:
Lots of good advice from seasoned climbers on here already.
Overall fitness - especially stamina and endurance - is one of your greatest assets.
As others have said, get plenty of mileage on multi-pitch trad - if the weather's crap, get out on long mountain Diffs and V Diffs in big boots and a sacs.
Speed can often make the difference between an enjoyable experience and a miserable epic, so work on covering easy ground quickly.
Scottish winters are superb for honing mixed skills, and getting used to poor conditions - you can still have good weather and poor climbing conditions in the alps.
Work on your efficiency as a pair regarding the technical side of things - quick, good rope work, slick belay changeovers.
'Head' fitness is as important as physical fitness, so be confident, but not overly cocky.
When it comes to alpine climbing, being able to climb VS trad and Grade 4 winter, quickly, all day long, in a variety of conditions, will get you up the large majority of alpine climbs.