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?
Your visa expired in February 2014. You cannot use that visa to enter the Schengen area after that date, so you must apply for a new one.
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.