Congratulations on your upcoming wedding and amazing European honeymoon! My wife and I went to Italy (Rome, Florence, Pisa, Venice) on our first trip to Europe in 2008 and to Paris in 2010.
Rome - Personally, I would start there as you have listed because it's southernmost. Completely understand the jet lag thing though, so maybe see something you wouldn't mind being a little hazy memory on that first day. Our bags were lost and I didn't sleep the whole way over, but we were so excited when we got there that we had to see something. Went to the Colosseum and to see Michelangelo's statue of Moses at San Pietro in Vincoli just around the corner. We ended up going back to both because I didn't really absorb either the first time. The only things I will personally skip the next time we go back will be the Spanish Steps and Palatine Hill. The Forum, Pantheon, Trevi Fountain, etc. are all neat. The fountain is crazy crowded, but it's still beautiful at night. However, a friend that just came back said it was OFF and under construction, so obviously check all things like that before planning your daily itineraries. Make adequate time for St. Peter's Cathedral & the Vatican museum. Just mind blowing the history, art, architecture, etc. Really took our breath away!
Florence - Quite possibly my favorite place in the world. I'm partial to Renaissance history, but the surrounding countryside is also worth every day for the rest of my life. Is that overstating it too much? Anyways, please do NOT waste a night in Pisa when it should be spent in Florence. Train from Rome to Florence, then half-day trip to Pisa (about an hour each way), then train to Venice. Easy peasy. However, I would consider cutting out Pisa all together to give more time to Florence, and this is coming from someone that dreamed about climbing to the top of the Leaning Tower for years! If the weather is good, get a picnic and walk up to the Piazza di Michelangelo overlooking the city and surrounding hills. I have many other specific suggestions about Florence, but this is already too long.
Venice - Are you staying on the island or the mainland? If you have the money, stay on the island. Not necessarily on the Grand Canal, but somewhere on the island(s). We didn't have the money, but we will make sure we do next time because we wasted lots of time coming from Mestre. Not far, but it added up. I don't care how touristy it may be, take a gondola ride. See if your gondolier will also take you down some smaller and quieter canals. Prepare to be gouged for the romance. We paid €70 for 45 minutes, but our guy told us about some history and sang. Don't miss St. Mark's Basilica and really stop for a few moments to take it in. We got lost a few times (not hard to do) and just had a great time wandering around with our gelato.
Our daughter's name is Italia, so yeah, we think Italy is cool.
Paris - After our whirlwind trip to Italy, my wife & I wanted to go to a city and really just get immersed in that culture. It sounds a lot like your trip to Spain. We look forward to seeing the French Countryside someday, but loved every second of our time as temporary Parisians. It was so nice to be able to slow down and let things sink in. We rented a tiny studio apartment just a few blocks from the Louvre and had the time of our lives! Loved Notre Dame (even if you're not religious, going to an evensong service is a beautiful experience), Saint Chapelle, the Orsay Museum, Rodin museum, among many others. Rick's Paris guidebook is on the money. See the Eiffel Tower at sunset/night or stroll Rue Cler and have a picnic in the park during the day. Both were unforgettable. Unless you're going to the top, I'd suggest staying away from the area directly underneath it. Really budget your time wisely at the Louvre. It's overwhelmingly massive. You will only see 10% of it so make sure it's the 10% you really want to see. I only have 50 characters remaining, so good luck planning the rest!