Well, you don’t say what interests you, so I’m unable to tell you what you should include or exclude. I dare say a lot of things will get left out anyway since you are travelling to five countries in a fortnight. France and Denmark are culturally different but quintessentially European: renowned cities, historic sites, great food, scenic countryside, fantastic repositories of art, and a whole range of activities from languid cruises to hiking trails. My suggestion would be that you read up on both countries and take a vote on what appeals most to your group.
I’m only able to go by the geography to arrive at this itinerary: fly to Paris, give yourself three-four days for the French capital and, perhaps, Nice, then head for Amsterdam (in The Netherlands) for two days of museums, walks and windmills. Next, take an overnight train to Zurich, spend three days in Switzerland, skip to Austria for another three, and finally head to Prague (in the Czech Republic) for a couple of days exploring its Vysehrad and Prague castles, Old Town, Jewish Quarter, Wenceslas Square, the National Museum (for its inspiring collections), and the Petrin Hill (for its views).
Divide your time in Austria between Vienna, Salzburg and Innsbruck, although it will be a horrid rush, and since Innsbruck is the farthest away, you could stick with Vienna and Salzburg (connected by frequent and fast InterCity trains in two-and-a-half hours), or Vienna alone.
The three days in Switzerland would be well spent in Lucerne (50km south of Zurich) with its rich museums and scenic environs. Or head for Interlaken and take the famous cogwheel train to Jungfrau. Mt Titlis and the Glacier Park are also hugely popular with tourists but a trip to them will need a day by itself. More choices to be made in the time available: historic Bern (90min from Lucerne) and its Unesco-protected architecture; Lausanne (100km to the south) and its lakeside panoramas; or elegant Geneva (less than an hour away) with its old town, flower gardens, cathedrals and boat tours.
I’m leaving two days out of my calculation: the comparatively inexpensive train connections will eat up some of your time, and if you don’t get a cheap flight out of Prague, you’ll have to return to Paris to benefit from a round trip booking ex-Delhi, a longish journey even on the fast European trains, with a changeover at Cologne or Mannheim (Germany separates your destinations of choice). You’ll find affordable vacation rentals for all your destinations at flipkey.com and vrbo.com, and Rail Europe’s India-friendly site is here: raileurope.co.in. The cheapest flight and train reservations happen up to three months in advance.