If you are renting in one country and dropping off in another the fees are usually considerable. You might also tweak the order of your trip a little (if your above post is reflective of the order) to Germany (unspecified destinations) > Hamburg > Amsterdam > Paris, so it's a more logical curve. Just a suggestion.

Lavandula

Did you mean to type, "do we rent a car OR take the train?"

Something to consider: you will be in three countries (Netherlands, Germany, France) and if you pick up a car in one country and drop off in another, the drop off charge can be very high.

Your itinerary is also a little short on detail, so it is hard to advise. If you are spending most of your time in cities, a car will generally not be that necessary.

"The train seems to take a long time"

Not only are drop off fees very high as mentioned, the trains are generally faster. Plus - if you plan on visiting mostly cities, a car will be virtually useless - no or very expensive parking, and difficult city center driving.

Thank you for the replies. We fly into Amsterdam, then with a group will take a train to Hamburg. We will be touring northeastern Germany with the group. When we leave Hamburg, we will have 6 days left to travel and make our way to the Paris airport. Planning the last leg of our trip is where we need some help!

You can use these sites to plan driving time and costs. It always takes me about 25% more time than the sites say it will. You also need to factor in time for stops on longer journeys.

viamichelin.com
mappy.com

You may think the trains take a long time but you need to figure out how much time you'll need for city driving, especially cities you're not familiar with. Where to find parking and how much it will cost to park your car when you're not using it.

When going from city to city, which you seem to be doing, I would recommend the train. You can pack a lunch, sit back and look out the window or read a book. It's very relaxing.

You could rent a car leaving Hamburg and drive around central Germany for your 6 days, returning the car in Frankfurt, or Stuttgart, etc., where you can take the train directly to Paris. No drop charges. That would allow you to see some smaller places flexibly, and efficiently, in the middle of your otherwise "big city" vacation.

Germany is the cheapest place in Europe in which to rent a car, and probably the most enjoyable in which to drive.

Between Hamburg and Frankfurt, for example there are many great options like Celle, Goslar, Wernigerode, Quedlinburg, Hannoversch Muenden, Eisenach, Bamberg, Wurzburg, etc..

With our trips to Germany, we have done a combination of trains and rental car - renting a car for any portion of the trip for which train travel is inconvinient. Travel by train or by car in Germany is very easy. Many towns in Germany are well-served by the train (even towns that you might not think would be on the train line) and the old town areas are very walkable. If the train station isn't very close to the old town, there is usually a bus and always a taxi service.

With 6 days left, I suggest that you simply take the train to Paris, which will take up most of the day. That leaves 5 days, or is it 4 because on the fifth day you fly home? Paris will take up all that time, or if you get tired of the city after three days, take a day trip (by train) to Chartres or Giverny (Monet's garden) or Versailles.

I was going to ask what Michael suggested. Have you been to Paris. If not you could go directly there as he suggested and either spend your time there or even split it between Paris and London. To muck up your plan even further take a look at skyscanner.com to see where you can get to by air. If you decide to stay and see Germany go directly to Bavaria, do not pass Go. You can rent a car and zip down the autobahns the check in your car and take an overnight train from Munich to Paris. Did anyone ask why you are flying home out of Paris? You can book open jaw from anywhere.

Lüneburg, Ratzeburg, and Buxtehude are among the interesting towns that surround Hamburg; you might look into those. 5 people can visit these places by train on a 9 am group ticket (good after 9:00) issued by Hamburg's transit authority, the HVV, and available from ticket machines:

http://www.hvv.de/en/tickets/day-tickets/9-o-clock-group-ticket/

On Saturday or Sunday the 5 of you can get a "Happy Weekend" daypass good for rail travel throughout the country:

http://www.bahn.com/i/view/USA/en/prices/germany/happy_weekend_ticket.shtml

Prices: HVV ticket, 24.90€ for 5; HW pass, 40€ for 5.