This is The Alleged Car, bought for Doug and Carrie by Arthur as a make-up gesture following a heated row about peanut butter. It is described as a typical product of Luxemburg and described by Carrie as " a soda can on wheels". The car is what Europeans would describe as "compact" and struggles to make sixty. The Douchenburger car appears in the episode Noel Cowards.
British viewers would recognise it instantly as a Mini Cooper, built in Britain between 1960 and the late 1990's. It even has its steering position in the intuitively correct place - for a country with left-hand roads. (Doug is clearly not at home with the driver's position being in the wrong place for the USA).
Its being redesignated as from Luxembourg - a tiny nation with no native car-manufacturing facilities which in reality imports its cars - is strange. Besides, Luxembourg drives on the right, like the USA, and the driver's position would then be on the appropriate side for the USA.
As a Mini might count as a classic car even in the USA, it's odd that they haven't realised its resale value to a collector might be quite high...