verge comes across as a bit literary but I think its meaning as mentula is widely understood by native speakers.

Vergus has indeed a more Latin feel to it than Bitus. The Oxford Latin Dictionary has :

• Vergilius : the name of a Roman gens, especially Publius Vergilius Maro (Virgil), the poet, 70 – 19 B.C.
• Vergīnius : the name of a Roman gens
• Vērus : a cognomen

enormus does not exist in this form in Latin, the correct form of the adjective being ēnormis. One of the translators decided to go full dog Latin, or latin de cuisine, as in English and came up with Bitus Grossus, the other one wanted to stay closer to actual Latin with Enormus Vergus. I think both translations work equally well.

My best bet is that the spoken French dialog has Bitus Grossus because it better matches the movements of the lips when Biggus Dickus is pronounced.

The subtitles haven’t this constraint and use Enormus Vergus because :

• it sounds more Latin (latin de cuisine precisely)

• is is immediately understood unlike Bitus Grossus which requires a small effort. (On the other hand, the reversed Grossus Bitus would have been a good alternative.)

Note that verge is not slang but the formal/medical name of it.

You’re overthinking it.
All foreign movies dubbed in French have different translations for spoken dialogues and subtitles. It’s never the same persons doing these translations.
Often, the French subtitles are the same in all French speaking countries but the spoken dialogues are different between French Canadian and French "Parisian".
They’ve never thought of making something consistent. It’s often difficult, for instance, to translate jokes.