channel crossing to Normandy

Well...first of all, it really would help to have much more in the way of specifics as to your proposed itinerary. Exactly how many days is the total trip? Are you flying into London or an Italian city (which one?) Leaving from...? Which cities in England and Italy do you plan to visit? For how long? Etc, etc.
Still, knowing as little as I do about what you intend, I can make a few general remarks. You really cannot drive from England to Italy unless (1) you are prepared to drive "on the wrong side" of the car when you go from England to the Continent or vice versa and (2) you are prepared to pay a gigantic drop fee or (3) you intend to backtrack to your starting point rather than flying open jaw, which would be insane. If you had not thrown in the question about the D Day battlefields I would say the obvious way to go from Italy to England or vv would be flying on a discount airline like Easyjet. It appears to me that what you really have in mind is England France Italy. But even at 21 days, that is a lot to cram in. Let me propose a 21 day itinerary which may or may not be useful to you in planning. Days 1-7 in London, with an overnight trip to Bath or York. Day 8, Eurostar to Paris. Paris Days 8, 9, 10. Day 11 Train to Caen, pick up rental car, drive to Bayeux. Day 12 D Day beaches. Day 13 return car at Caen, train to Paris. Day 14 fly discount airline from CDG or Orly to Milan, Venice, Pisa, or Rome and spend the remainder of your time in italy, flying back to the US from one of those cities. If you are serious about going to Europe, go out now and buy RS 2011 Best of Europe, and read the first part and study the maps in the front of the book. You will find that book invaluable in planning.

Travel plans within England and Italy have been made. I am inquiring about which ports with ferry/hydrofoil for the Channel crossing are closest to the D-Day beaches. Will we have to go to Paris to get train service to Florence? What is the travel time by train between the two cities?

You might have gotten more responses if you have posted this on the "West" or "Transportation" sections of the Helpline, but still... If you are determined to take the ferry across the Channel, I suppose the closest to the D Day beaches which, keep in mind, stretch across 50 miles of French coastlinewould be Ouisterham (Caen). The English port of departure would be Portsmouth. However, once you get to France, you'll have to take a taxi to the nearest rental car agency. To get around the beaches, you'll need a car or else a reservation with one of the tour companies that pick up from hotels in Bayeux or Caen.
To get from Normandy to Florence by train, you'll have to transfer in Paris. Even driving, and again, it would be a very long drive and you would have to pay huge drop fees if you drove the car to Italy you would pretty much have to come around Paris on the Peripherique or else do a very long cross-country trek. Ed, who drives all the time in France, can better advise you. There is a direct overnight train Paris to Florence...but reserve at least a couchette in advance, and be sure you can sleep even on a berth in a moving train (I can't). By day trains, you would take the TGV to Milan, then go on to Florence (total travel time probably around 8 hours). Google the "Man in seat 61", a website that has tons of info on train travel in Europe.

Regarding the driving and the ports in northern France: Rather than leaving from Portsmouth, I feel you'd be faster and cheaper to take the train to Dover, ferry to Calais, rent a car at Calais and drive to Caen/Bayeux. The ferry ride is an hour and a half. It takes three hours to drive from Calais to Caen/Bayeux. It's been years since I've ridden the London - Dover train I have no idea how long it takes. I think there's a way to take a train from London to Calais, but I've never done it, I think the departures are less frequent, and I think the total price is higher. That's a lot of 'thinks' and I might be all wet. While I nixed Portsmouth, it has a lot of merit: HMS Victory and the Royal Marine Museum come to mind. Directferries.co.uk is where I figure out all my ferry business. If you're going to spend a whole day positioning yourself from London to Caen via Calais, you'll have plenty of time to stop for a couple of hours in Rouen (Lionheart's heart is in the cathedral that Monet painted so much, the death site of Joan d'Arc is a couple hundred yards down the street). You could also stop for the night in Honfleur and be only an hour from Caen.

Without a guided tour in Normandy, you have to have a car. I can show somebody the area pretty well in one full day and catch the tapestry museum as well. I can't fit in both the Caen and Bayeux museums they have to pick one. FITW I was up that way last year with a buddy who's a former director of the Marine Corps Museum and he says the Bayeux museum is the better of the two and he was comparing them rather closely talking to management, etc. Regarding driving across France: I have no inkling of what you want to see in France, but the drive from Caen to Milan would be a really hard twelve hours (maybe more) that's with gas stops and nothing else. That time of year, you'd also be going through the mountains when it's dark and you're tired plus you'd miss the scenery. The second-country drop-off charge would bust my budget. Take the train, as Roe said. Edit: The peripherique is going to be a bear coming in from the north at the time you'd hit it (considering a close-to-dawn start). You could duck it by cutting a bit west toward Versailles, but that would probably be even worse. Either way, it could add a couple of hours to the drive - - it just depends on what's going on.