'Gran Turismo' is for sure italian.
The french equivalent is 'Grand Tourisme', the english one 'Grand Touring'.
Racing competition makes a distinction between cars designed for racing (known as prototypes, racing cars...) and cars originally designed for a road use. The latter are called 'voitures de tourisme' in french ('touring cars' in english).
Among them, the top of the category are called 'voitures de grand tourisme' ('grand touring' in english, 'gran turismo' in italian)
Many championships involving road cars use this terms.
'Touring car' in :
- DTM (Deutsches Touringcar Meisterschaft)
- BTCC (British Touring Car Championship)
'Grand Touring' in :
- JGTC (Japanese Grand Touring Championship)
The terms GT has also been widely used for naming many sport cars (Opel GT, Porsche GT2...) and it has a positive meaning associated to sport and performance.
Pretty much like the 'A-spec' term in Japan.
Of course the game features cars from all 3 categories, but the term GT was chosen for the meaning I just mentionned.
(The longer this post gets, the less clear the explanation sounds to me, so I'll stop right now)