Leanna-
If Paris, Normandy, Rome and another location in Italy are your must dos - it is doable
I have nothing against multiple countries in a 2 week trip.
I flew to Vienna 4 nights>>train to Budapest 3 nights>> flew to Berlin 4 nights>>flew to Amsterdam 3 nights with my daughter a few years back. More moving/flying then I'd do with my husband but it was on her dime and it was a great trip.
Divide your time almost equally between France and Italy. Keep your transits as simple as possible, this is your first trip.
Normandy as a day trip from Paris is an extremely long day - if you really want to see the beaches and get the most out of that area then plan to spend 2 nights there. Highly recommend taking an all day tour of the Normandy beaches- you will get so much more out of it, very hard to do on your own and almost impossible without a car.
We used Bayeux Shuttle and were very pleased.
(We spent 4 night in the area- 2nd trip to France and had a car but still did the guided tour)
Pick Tuscany OR Amalfi. I’d lean towards Tuscany just because it’s a bit easier to get to and from. Amalfi is fantastic with so many sights to see- really needs more than the 3 nights you have to give it, especially when you add in the time it takes to get there. (We spent 9 nights in the area but that was a 2nd trip to Italy)
Something like this:
Fly into Paris- train to Bayeux 2 nights
(You’ll be jet lagged first day anyway might as well get moving.
Visit Bayeux town, don’t miss the Tapestry! next day do your WW2 tour.
Train to Paris 4 or 5 nights
Fly to Florence 3 or 4 nights-with a day trip or 2 to Tuscany hill town of choice
I’m guessing there are cheap flights to Florence. We did love Montepulciano but it doesn't have train service- you could do Florence 2 then get a car for 2 nights but that is just more to figure out and not sure how comfortable you'd be driving in Italy as first timers, there are lots of other hill towns that are easier to visit by train- Siena, Lucca, etc.
Or you have the option of bus from Florence to Montepulciano- then bus or bus/train to Rome
Train to Rome for your last 4 or 5 nights.
Fly home from Rome
I like to use www.rome2rio.com to check out transportation options
Do not book your flights yet. You have homework to do first.
Excellent advice from David