If you have the possibility of travelling from Italy, this is an option that might be worth checking. The Italian railway is currently running Smart Price deals on tickets for international destinations. Nice, which has direct and very regular connections to Cannes, is included in the list, with prices from Milan starting at €15 (Naples, Rome and Venice can be reached from as little as €35 in an overnight couchette). Conditions apply, needless to say. For details and booking in English or Italian, visit Trenitalia Smart Price.
Since this piece was published, another service has started connecting Marseille with Milan, Thello. Check this item for details.