There are direct day and night trains (with sleeper and couchette carriages) from Sicily (Siracusa / Catania and Palermo) to Roma (the whole train goes by ferry). There’s also a direct night train to Milano.
Roma to Firenze and Firenze to Milano has frequent high speed services.
There’s a direct train from Milano to Paris in the afternoon, but because of a landslide there’s a bus replacement in between (but it’s still shown as direct connection). It’s also possible to go via Genf (Switzerland) to Paris, but there is a bus replacement in summer, too (on the italian part of the trip). But it’s possible to go there earlier in the morning. It’s also possible to go entirely by train via Lugano (Switzerland) (takes about 10h).
Paris to London has frequent Eurostar services.
In general, all long distance trains on this route do require a mandatory reservation.
Timetables for summer aren’t published yet, but you may check a current date to get an idea how the timetable will look like.