After many frustrating hours on the internet, I have discovered the following useful fact.
If you want to travel from Italy to anywhere in France, or from France to Italy, do your research at http://www.trenitalia.it/ . While the SNCF site will only tell you about the 2 trains a day that run from Paris direct to Milan at times that no sane person would want to travel, Trenitalia gives you all the options, including journeys with changes in Switzerland and Germany. Even more bizzarely, on the Italian site, you can research journeys from Milan to cities in France other than Paris, while the SNCF appears to believe that no foreigner wants to go anywhere other the capital.
So take heart, mes amis de la France profonde: Paris may be too self-absorbed to acknowledge your existence, but the big hearted Italians still care. Un abbraccio a tutti!