An excellent resource to figure out trains in Europe is the "Man in Seat 61" website.
In your particular case, you have a few choices:
- Paris to Milan = either with SNCF (French railways), whose app is SNCF Connect, or with Trenitalia (Italian state railways).
- within Italy: either with Trenitalia or with Italo (Italian private railway)
And in each case, you can use the respective train company's app or website. Bookings for the Paris-Milan train open about 4 months ahead, and I am not sure of the current booking windows in Italy (but it's probably either 3 or 4 months). The earlier you book, the cheaper, and cheapest tickets for Paris-Milan definitely cost less than airfare.