The Quirmian connection(1) to Genua is not explained. Perhaps it was colonised in early times by Quirmians, or it may have developed a relationship later. In any case the language of Genua is a form of Morporkian salted with a good deal of Quirmian and the culture draws on Quirm as well. The great river that flows down to it from the mountains of Überwald is thus named in a Morporkian style translated to Quirmian.
"Mon vieux" is used in Quimian just as Morporkians (at least in Rust-de Worde- Selachii circles) might call each other "old man", or "old boy". As Nanny Ogg mused, in foreign parts even the words have sex. Granny Weatherwax was not surprised. The Multiverse seems full of Oldman rivers and Old Man Rivers, and when one of these becomes deep and broad enough it will naturally develop a certain style of paddle-wheeled river boat to carry the coal and iron and grain and meat down to the warm sea and the sub-tropical produce back up. People will begin to write songs about it and picaresque stories of Life On The River.
It might be surmised that, as in ancient Roundworld, certain rivers have attendant deities who are essentially synonymous with the watercourse. If the Vieux River has one, he must know somethin', but thus far he don't say nothin'. He just keeps rolling along.
The city of Genua is on the delta of the Vieux where it reaches the Swamp Sea. A riverboat trip to Genua is described in Witches Abroad in which we learn not to play Cripple Mister Onion for money against naive-seeming elderly women carrying broomsticks.
(1) Little movie joke there, erm...