First of all, I hate you. You're going to Europe and I'm not. :-)
Seriously though, if possible check into storing your bike boxes at the airport. I've stored bike boxes in Milan Malpensa and Frankfurt. It's only a couple of Euros a day and was well worth the cost. You will get charged per piece of luggage, but you may be able to consolidate them into one if they are the clam shell style. Even if you can't, it's worth to cost.
As somebody else said, get the international drivers license. I rented a car in Italy and was not told of this and wasn't asked for one either. But I got pulled into a check point leaving the Dolomites and heard a lot of "non va bene" from the police officer. He finally let me go as we had an injured friend who we were taking to Malpensa and we were leaving Italy for France and maybe partly because he was tired of talking to the stupid American. :-)
If you can get rid of the bike boxes a wagon will work fine. I also agree with the GPS as others have mentioned. Though we had a hell of a time finding our hotel in Briancon in the dark inside the walled city with it. If you have a GPS it might be cheaper to get the Euro maps for yours and also nice as you'll be used to using it. Using your phone is another option but roaming data is hideously expensive. You can get a roaming data package (and you should even if you don't use much). Also, if you've got an Android phone I believe you can set up your route over wifi and save the maps you'll need for your trip so that you don't need to use data while you're driving.
I don't know about Luxembourg, but here is a tip about diesel if you get a diesel car. In Italy there are two grades of diesel and one of gasoline. In France there are two grades of gasoline and one of diesel. And in french the word for diesel is something like gazzole. Can you see how that might be an issue?! :-)
Good luck and enjoy your trip.
Kevin
http://kevinmetcalfe.dreamhosters.com My Strava