First trip to Europe - seeking advice

Tim, are you in Melbourne, Australia, or Melbourne, Florida?

I don't have any experience looking at airfares between Australia and Europe, but the conventional wisdom is that a multi-city (open-jaw) flight such as you need will be about mid-way between the two ordinary round-trip prices. However, fares are highly date-specific, so to check this out you should play around with the exact travel dates you have in mind. In addition, I think the multi-city flights sometimes are costlier than expected when the two European gateways are served by different sets of airlines. In that situation you can also run into awkward routings with an uncomfortable number of connections. Basically, you need to take a look. I use Google Flights for information then book through the appropriate airline; others have their own preferred flight websites.

If you are in Melbourne, Florida, you should also consider whichever budget carrier flies out of central Florida. I think it's Norwegian Air, but it might be WOW or Icelandair. Others on the forum can help there. The flights of the budget carriers do not show up on Google Flights, so they have to be researched separately.

From my origin Milan is nearly always one of the cheapest options in Italy, and Paris is a competitive route so also not too expensive. But your origin is different.

Most people suffer from some jetlag when they first arrive in Europe. Many of us also don't get any sleep on the overnight flight. So I urge you to arrive in Italy at least 24 hours before the initial race activities you want to attend. Figure your arrival day is going to be spent walking around outdoors, trying to get adjusted to the new time zone. Some people continue to feel "off" on the second day, so depending on how important the race is to you (I'm guessing "very"), you might want two days of padding at the beginning of the trip.

I wouldn't want to travel all the way from Italy to Paris to spend just two nights there at the end of the trip. That would give you only about 1-1/2 days in Paris. I'd either fly, hoping for 4 nights, or spend the post-cruise time in Italy (Florence? The Lakes? Turin?). I'm sure you'll fall in love with Europe, agnd Paris--and all of France--will be waiting for you on Trip #2.

I've never taken a cruise, but others here have. If you post the ports you're considering, you may get some useful comments about which ports are better located vis-a-vis the places where you'll probably want to spend your port time. You should also check out a cruise-specific forum. Here, we tend not to be such great fans of cruises.

Assuming Melbourne Australia, it is still early to get airline (wait a couple of months). Looking out almost that far, 1700 AUD to Milan and return from Paris looks to be reasonable using Qantas or Emirates, changing in Dubai. It is not much different flying round trip to either of those cities.

Genoa is the closest port to Milan, but if you want to visit elsewhere in Italy, see what cruises there are from Livorno (Florence and Tuscany) or Venice. Both are easy and frequent train rides from Milan. You might also look at Varenna on Lake Como, which is just north of Monza less than 1 hour on the train.

Genoa to Paris is at least 9, and more often 10+ hours by train. Some routes go through the Alps (with tunnels) and some along the Mediterranean coast to Nice and then TGV to Paris. Consider flying. And more time in Paris is better than less.

You really need to look at cruises out of Rome.
Best fares for next year to Europe from Australia are 'earlybird' deals available Nov-Dec.
Fly in to Milan and out of Paris. Singapore Airlines may be a good option.

Something like this ...

Aug 30. Arrive Milan (4 nights) for F1 Monza
Sep 03. Train to Rome (5 nights)
Sep 08. Celebrity Cruise (10 nights) from Rome to Barcelona
https://www.celebritycruises.com/spa/#/itinerary-details?packageID=CS10M187&sDT=2018-09-08&cCD=CO&aCB=false
Sep 18. Barcelona (4 nights)
Sep 22. Train/fly to Paris (5 nights)
Sep 27. Depart Paris

For your trans-ocean flights you can use the “multi-destination” function on many travel agency Internet sites. Many airlines also offer this combo, sometimes called multi-city. Fly into one city, fly out of another. These are not one-way tickets; they are booked together. They often cost almost the same as a simple round trip, plus you save the time and expense of returning to your city of arrival.
To shop for air fares, you can start with matrix.itasoftware.com It is run by Google for airlines and does not sell tickets but you can use the info to go to the airline sites. Or you can buy from many retailers such as Expedia or Cheapoair. They can put together sets of tickets from airlines which don't sell each other's fares. No site covers everything with wings.
To explore internal European flights, www.skyscanner.com It covers the no-frills lines that operate on single-flight-only schedules, no connections even to their own planes. Some of the older airlines compete for price against these budget lines.
For all railroad information, the treasure trove is www.seat61.com
Everything in central Paris is relatively easy to access by using the rapid transit system. Rather than aiming for a landmark – the Eiffel Tower area is fairly inconvenient, for instance – I look for a Metro subway station near a hotel in a less touristy location. A main station serving more than one line is particularly useful.
Rapid transit, including trip planners: https://www.ratp.fr/en