Hamburg

If you are married to Delta, take a direct flight to Frankfurt. There is a direct train from Frankfurt Airport every 2 hours to Hamburg, taking about 4 hours. See if Delta participates in Rail-n-Fly and you get get the train of your choice for a low price.

Edit - Unfortunately they do not, but Lufthansa also has direct flights from DTW, and they do. They seem to match Delta's prices to the $, so that is an option. Cost is $42 US per person for on-going train ticket.

CDG is not a good idea since you will loose a day in transit (9-11 hours). Even FRA to Hamburg is 4 hours ore more by train. I'd search for direct flights or, if there are no convenient ones, for flights with one transfer at any maior European airport (personally, I'd prefer FRA or Schipol or Copenhagen and avoid CDG or Heathrow). Both flights have to be on one ticket to avoid problems in case your transatlantic flight is delayed.

You have the choice of flying on both legs or taking the ICE train from Frankfurt Hbf. Fly to Heathrow or Frankfurt, then connect to Hamburg if you want to get there by air, depending on your time constraint.

We faced the same problem for our trip to Hamburg starting this week (May 3, 2018). We finally decided to fly into Amsterdam Schipol and take the train to Hamburg with a stop in Cologne to sightsee, especially the cathedral. It does make the trip a full day but the hours in Cologne should be worth it. On the return we will be flying on Eurowings directly to Schipol to connect to our flight home. Tickets for both train and plane were very reasonable when purchased well in advance. I think the train was about $60 and the flight was about $125.

United Airlines has a non-stop flight to Hamburg Germany from Newark NJ (EWR). That would be an option.