Exactly what's available to you does depend to a large degree on the weather you face. There are several passes through the Alps, with the one directly West of Turin being a good option (I've flown this in an R44). You will need to get up to 10000' AMSL to get over the Italian end, route past Chambéry on the French side. There are a number of friendly airfields in the South of France (who will also deal with passport stuff). You can then work your way North to Le Touqet (stopping as you wish/need), where you fuel up to hop the channel to Lydd. Then you route as necessary in the UK.
Alternately, you can route around the South coast, via Genoa, Nice, Cannes, etc. This route is much less weather dependant, but I believe landing fees etc. on the South coast are steep. Once you're around the Alps, route through France as above.
Dunno about the N-reg part, tho; are you planning to move it to the G register? If so, it might make life easier to get it done before you fly back, if at all possible. Alternately, it may be easier if you hold a FAA license. No doubt, someone who actually knows about N-reg machines in Europe will chime in shortly
For reference, Denham - Lydd - S.France (can't remember which airfield) - Alps - Turin is about 5 hours flight in an R44, with perfect weather. Can be done in a day when you include fuel/paperwork stops.