Gran isn’t a French word.

When Google Translate does not know a word, it leaves it unchanged.
Even worse, sometimes it outputs an English word, because the translation goes through the English language. (I saw it the other day but it has been fixed.)

About the examples you listed:

• Gran Turismo is a computer game about driving.
• un gran fan is a typo, should be grand.
• Gran Sport is a Bugatti car.
• “Forts d’une gran” is a sentence that has been cut by a dash and a new line, the rest is “-de expérience”, that is “Forts d’une grande expérience”.

More generally, Google can find examples even with words that don’t exist, like “radiohead” or “satelite” (one L missing).

In a nutshell: don’t trust blindly Google translate, double check on word reference.

I have no proof of it, but I am under the impression that the adjective you mention may derive from the usage there is for it in Italian.

Actually, the adjective “grande” can be shortened to just “gran” when used in connection with masculine terms. For example, you could say Egli fece un grande/gran rumore aprendo la porta (He made a lot of noise while opening the door), but the preference would be for the second option, and surely nobody would ever say grande ciambellano instead of gran ciambellano or grande visir when talking of the relevant positions at court.

I know it is not relevant to French, but perhaps this could explain the usage of gran in some expressions.

In deed, “gran” is an Italian adjective (in short form) which translates into “grand” or “grande” (French) or “great” / “grand” (English). It comes from the Latin “grandis” through the old english “graunt”.

It doesn’t exist in French so Google translation didn’t translate it….

Gran Turismo is a proper name, but it is Italian. In French the equivalent class (GT) is also called Grand Tourisme.

“je suis un gran fan de Stromae” is incorrect (wrong spelling). Corrected : “je suis un grand fan de Stromae”

“gran sport” is a proper name and probably meant to be italian (like the Ford Gran Torino).

C’est une erreur de transcription, gran n’existe pas en français, seuls grand(s) et grande(s) sont valables, et vous avez eu le bon réflexe de vérifier.

Lorsqu’une traduction ne me convient pas, que je la trouve bizarre, ou encore que la contre-traduction donne n’importe quoi, je vérifie avec (ici en anglais, mais d’autres langues y sont disponibles) :

• linguee pour comprendre l’utilisation ou saisir les nuances selon les contextes.
• un regroupement de traducteurs quand il s’agit de phrases particulières. En général, il y a au moins une phrase qui donne une réponse cohérente.