If your visa is already valid on December 15, you can go to Italy immediately after entering France or even enter the Schengen area through Italy as a long-stay visa from a Schengen country also allows its holder to cross any external border without Schengen visa and to stay for up to 90 days in any 180-day period in another Schengen country.
But with a French student visa, you need to register with OFII within three months of first entering France and you will be asked to come for a medical exam. You should have received a document about this from the consulate. As far as I know, there is nothing illegal about going in and out of France during this time but you have to send the form in a timely manner and remain available for the exam whenever they call you.
Formally, I think the three-month clock only starts ticking when you enter France, not the Schengen area, but if you enter through Italy it will be more difficult to prove that you did not enter France shortly thereafter because you won't get a stamp when travelling between Italy and France. So I would recommend handing in your registration to OFII within one or two months of entering Italy.