I have been issued a multiple-entry type C Schengen visa from the Italian embassy. But it is not valid anymore [OP: "already"], only from October 2013 to February 2014. if I am planning to go to Paris in January 2015, can I used this visa or I should apply for another Schengen visa from the French embassy?
The problem is, you'll arrive at the airport, go to immigration, and show them your passport. They'll look for a valid visa. You won't have one as your visa (from their point of view) has expired. They'll then turn you away at the border.
If you even get that far - the airline when you leave will likely stop you from travelling in the event you don't have a valid visa.