The international versions have some English text replaced by text in the local language. For the DVD it becomes the language that you choose upon inserting the disc. The replaced text includes for instance Doc's newspaper clippings, the "Closed" signs in Los Angeles and the "Lead lap" text during the last race.
In the French-language version, the joke about "Mater, like Ta-Mater without the 'Ta'" did not translate, so Mater was renamed Martin, and the joke became "Like Aston Martin without the 'Aston'."
Since the movie has lines in Italian, the Italian release (where foreign movies are mostly dubbed) was handled with a twist. Luigi was dubbed with a slight Modena accent (the home town of Ferrari) and Guido was dubbed with a thick Modenese dialect. The Ferrari in the end of the movie has been dubbed by Michael Schumacher as in the original version (but of course in Italian, with some German accent). Giancarlo Fisichella makes a cameo. A nice coincidence: Marco Della Noce, who dubs Luigi, is an Italian comedian whose trademark act (several years before the release of Cars (2006)) was playing of the head mechanic of Ferrari, and includes some of the lines from this routine in the dubbing.
In the Danish version "The King" is renamed "Tom Kilerem" and is voiced by 7-time Le Mans champion Tom Kristensen.
In the German-language version of the film, Mario Andretti is dubbed (and his character name is changed to) 2-time Formula One World Drivers Champion Mika Häkkinen. The character "The King" is spoken by 3-time Formula One World Drivers Champion Niki Lauda.
The 3D version, as well as the 2013 DVD & Blu-ray releases, replaced the Disney logo and its music cue with the more elaborate current logo.