Flights are booked. Now what?

I would do Paris 7 days (including a couple of day trips somewhere it depends on your interests)
August 20-26
Fly to Budapest for 3 days
August 27-29
Train to Prague for 3 days
August 29-Sept. 1
Fly to Amsterdam 1 day
September 2
Fly home
September 3

I agree with cmorgan7france. With seven days in Paris, that leaves time to break up the city with day trips. You can day trip to Brugge, Belgium, a tour of the castles of the Loire Valley, Mont St. Michel, Normandy beaches and so many others. When I took my wife, her first time in Europe, we day tripped to Brugge and the Loire valley, there you can see the different castles. The castle tours may visit different castles on different days. I would not take more that two day trips from Paris. I love Paris but you can get tired of churches and museums. I would space the day trips at least a day apart.

For the Loire valley, we took a train to Tours, walked across the square to the tourist information office to meet the driver. We left early I think close to 8, had lunch in the city of Ambiose, and then were returned to the starting point. We had enough time to grab a few sandwiches and drinks for the train ride back to Paris. In Paris, we walked to the Notre Dame and just sat eating gelato.

My wife liked the difference between the big city of Paris and the smaller city of Brugge and then the Castles of the Loire Valley. But if castles are not your thing then skip it.

Different places in Paris are closed on different days. This may present a good day for a day trip because everyone else will visit the remaining open places that day.

If you spend seven days in Paris, I recommend a Paris Guide book.

Feel free to come back here or visit the specific countries forums for more detailed information. There is a great wealth of knowledge on these forums.

I'd try and squeeze in a short stop for Vienna.

Paris - 4N
Fly to Budapest - 3N
Train to Vienna - 2N
Train to Prague - 3N
Fly to Amsterdam - 2N

Your itinerary has two flights and a long day of train travel, not very efficient. I've researched the heck out of trips between Amsterdam and Paris since I like KLM/Air France direct from the West Coast. One suggestion is Paris, Provence, Barcelona, fly Amsterdam. One flight and some manageable train rides. I'm booked for my third trip and this time we are flying Amsterdam to Rome but skipping Rome and heading to Tuscany. We are taking trains stopping in Burgundy on our way to Paris. I've traded one long train day through Switzerland for the second flight.

Something like this would reduce your internal European flights from 2 to 1.
Paris - 4N
Fly to Prague - 3N
Train to Dresden - 1N
Train to Berlin - 4N
Train to Amsterdam - 2N

Noting that Richard (LA) made a complementary suggestion.
Paris - 4N
Train to Provence - 4N
Train to Barcelona - 4N
Fly to Amsterdam - 2N

Thanks for all the suggestions. Barcelona is out because I'll be spending a week in Spain in May. There's a train that leaves Paris late afternoon and connects for to an overnight sleeper train in Zurich to Prague. I don't remember the exact times but I believe I would leave Paris at about 5:00 in the afternoon and arrive in Prague at about 10 am. So I'm leaning towards that because it'll cover a hotel and transportation in one cost and take up minimal sight seeing time. It's an easy train from Prague to Budapest, but yes I will need to fly from Budapest to Amsterdam if we choose to stick with that itinerary. Berlin is still an option for us, as is Vienna and Switzerland. Luckily we have plenty of time to iron out the details of our trip.

Jeremy, take a hard look at the details for the night-train itinerary you're considering. I think I found the one you're thinking of on the Deutsche Bahn website, and it looks like the train will make about 20 stops between Zurich and Prague. For me that would be a miserable experience.

You could spend a day exploring medieval Bern before getting on the night train in Zurich.
Paris - 4N
PM Train to Bern - 1N
PM Train to Zurich for Night Train - 1N
Prague - 3N
AM Train to Budapest - 3N
Fly to Amsterdam - 2N

acraven that's true, I checked the Czech railways site and there are a fair amount of stops but no transfers. My only thinking is that for 200 euros my wife and I can have a private room and leave Zurich at about 9:40 PM and arrive in Prague at 10:30 the next morning. Save a hotel bill,not have to pay/ hassle with getting to and from the airport, and not lose much valuable daylight that could be used for enjoying the cities we're in. Still a lot to consider, that's a lot of stops. We've always slept GREAT on night trains but those stops may be excessive. Thanks for the heads up!

Jeremy, you may be OK on that route. When I was younger I took some night trains and slept in couchettes. They weren't great, but I was horizontal and I did get some sleep. The main problem was that I was often cold, because my bunk was always on the side of the compartment toward the back of the train, and inevitably someone wanted the window open!

But in 2015 I took an utterly miserable night train from Rome to Catania, Sicily. The tracks were not remotely smooth and the train jerked constantly from side to side. I don't think I'd have slept even if I'd had my own sleeping compartment. I arrived exhausted and it was many hours before I had a bed I could collapse into. That first day in Sicily was like the day after a trans-Atlantic flight.

It definitely seems like it can be hit or miss according to all the reviews I've heard about night trains. I took them twice, once in a private two bed with my wife from Amsterdam to Munich and again in a 4 bed couchette with another couple we travelled with from Munich to Venice. Both times we slept great, the second trip the couple we were with not so much. Although I think a lot of it had to do with how tired we were from all we did on the vacation. Looks like I'll have to dig more into the prices and time compared to flying and figure it out. I appreciate the feedback. You'll probably be seeing plenty more questions from me as I get to planning the trip. I've got Hong Kong in March, Spain in May, then two weeks back in Europe in August.