If you are not planning on taking a train or flying from France to Italy, or you would like to book the cheapest route, traveling by bus from Paris to Milan is the best way to go.
A company called Eurolines offers regular coaches from Paris to Milan. Their buses leave Paris Gallieni bus station for the Milan city center once a day at either 18:30 (M, W, F) or 22:45 (Tu, Th, Sa, Su). Services arrive in Milan the following morning at 7:15 or the following afternoon at 14:00, respectively.
The bus ride from Paris to Milan takes 12 hours and 45 minutes or more, depending on whether traffic is light or heavy and when coaches depart. Delays are common, so keep that in mind if you are connecting in Italy.
Tickets for Eurolines buses from Paris to Milan can cost from 24 euros for singles if you book your tickets online at least 30 days ahead of time.