"I hear that the Eurail Pass will work for me. "
Alas, you've heard wrong, which is why you're so confused! Whoever promoted Eurail Passes years ago was a genius; now that they're not a good deal for most travelers, they are still the only thing that anyone's heard of for European train travel. For your itinerary, you'll do much better with individual tickets.
As you have been told above, for your trips within Italy, there are two rail companies that make these journeys: Trenitalia http://www.trenitalia.com/tcom-en and Italo http://www.italotreno.it/en. Each has advance purchase non-refundable tickets that are cheaper, but full fare tickets are not that expensive. Any ticket for these routes - discount or full fare, bought in advance or on the day of travel, bought on line or in a station - includes the required reservation.
So, look at those websites for your travel dates. Use the Italian names of the main stations for each city:
Rome - Roma Termini
Florence - Firenze Santa Maria Novella (Firenze SMN)
Venice - Venezia Santa Lucia (Venezia SL)
If you pick a particular train and click on the details, you will see if there are discount tickets left and what the restrictions are. You can also see the full price. If the full price is acceptable to you, no need to buy in advance. If you can accept the restrictions on a discount ticket, book now for the savings. Either way works fine.
I agree with flying from Venice to Paris. Just note that some airlines use the "real" Venice airport (code VCE), and others use Treviso airport (TSF). Both can be a bit of a pain to reach, particularly for an early flight; research options for getting to the airport in time for your flight, before booking. Similarly, Paris has three airports. Orly (ORY) is smaller and closer to the city than Charles de Gaulle (CDG), but both work fine. Beauvais (BVA) is much farther from Paris. To find flight options, use Skyscanner: https://www.skyscanner.com/