Nowadays the people of Menton have more in common culturally with Parisians than they do with the people of Ventimiglia (who live less than 7 miles away), who themselves have more in common culturally with Sicilians. Yes, the landscape and architecture are similar, and they have a share history–but then there's: Language; non-verbal communication; popular culture; education system; legal system; the press; humour; food and drink; daily habits; shops and shopping; smoking; levels of formality; the nuclear vs. extended family; young person autonomy; diversity; the legal system and many laws; local, regional and provincial government; bureaucracy ... (I could go on ad nauseam.)
I think that it's an excellent idea for the OP to consider a day trip to Italy–even if its just to get the slightest taste which could inspire a future, lengthier and more rewarding visit.