There is no night train from Paris to Copenhagen but there are night trains within Germany and also night trains from Hamburg to Copenhagen which can be used on the route from Paris to Copenhagen. The time tables for December are not yet released though. 

Ok thanks. Then I guess I am looking for an option of going through Germany to Copenhagen. I may have to purchase a ticket from Paris to somewhere in Germany to get the overnight train??

You could get with an TGV/ICE to Karlsruhe and from there with the nighttrain to Hamburg. From Hamburg there are trains to Copenhagen. You could also go to Basel (Switzerland) and take there the same Nighttrain. 

Will you travel only to Copenhagen and Paris? Maybe you can add a city to your plan so it is better to get trains or nighttrains for your Trip. 

Also 4-berth REAL sleepers does not exist here-yes in Eastern EUR, where you will not want to be now-its 3 max and single sex if no family ties

What is called couchette (liegewagen in german) is a kind of budget option- with 6 fold down bunks (rolling dorm) that in some cases is also offered as only 4 taken=more space, but same compertmt.

ON seat61,com are far more pix and expalnations.

There are talks about reinstating some of the classic old nighttrains-but as for now only  Hamburg-passes K/obenhavn around midnite-to STOckholm is in the cards.

You may find on planners an overnite from say FRankfurt or Köln to Hamburg=thats a normal daytime train ICE with seats only. As for now there is simply NO offer with sleeper/couch. along this route.

There is one-called NightJet from Swiss (Basel) to Hamburg-its a bit out of the way, but with a pass thats no prob-that might suit you if fancy this idea-the total trip will then be just short of 24 hrs with train before from P and on HH-K/ob.

Also all rail-timings change 2nd weekend in dec-timings for after that are only released a  few weeks before-for general rough planning use a samedayofweek now.