Yep, need the breathalyser kit for france (comes as a pack of 2), available at most ferries or Eurotunnel, or online from AA, RAC, ebay etc.. only other bits you need are warning triangle, spare bulbs and hi-vis vests, + motorway 'Vignette' for Swizterland and Austria. you shouldn't need snowchains this time of year
The alps really aren't that far, mind you coming down from Scotland will add a bit. It looks like there's a Hull to Zeebrugge, Belgium P&O ferry which will get you straight into the right area.
Area round Zurich is lovely, Zurichsee coast road quite scenic, but very slow and flat. I'd personally head to the Black Forest first then onto the mountain passes. I'd head to Strasboug (easily done in 5 hours from Zeebrugge), then over the border into Germany to Offenburg and some amazing roads using the 33 and 500 down to Switzerland.
The mountain passes are mostly French/Swiss or Italian/Swiss border, so all maximum of a day apart. Once down near Zurich you can go South West to checkout San Bernadino, Splugen pass, Fluella pass, Maloja pass, and Stelvio or course.
Going East back toward Geneva and France you got Col du Pillon, and the amazing Col de Turini (as featured on the Monte Carlo Rally) and from Grenoble down to Nice is The Route de Napolean.
The Italian lakes are well worth checking out if you fancy going a little further south. Very memorable moment of leaving the light snow at 2 degrees C at Stelvio, at 9am and driving a few hours East and having lunch in shorts by the very lovely Lake Maggiore at 28 degrees C.