Star Alliance members such as Air Canada, Lufthansa have round trip airfares travelling from Dallas (DFW) to Copenhagen Denmark (CPH) for $325-$354, making 1 stop. I have both screenshots attached so you can see for $325, you'll have a longer stop with Air Canada or for not much more, you'll be on Lufthansa. I prefer Lufthansa honestly.
Departs DFW: Jan 17, 24; Feb 7, 13, 14, 20, 27; March 6, 7, 14, 21; April 4, 11, 18, 23
Returns: good availability returns using a 6- 11- or 13-day turnaround
To book this, enter travel information on Skyscanner [skyscanner.com]
and then select your flights and favorite OTA to book with. For hotels, check out Hotwire's Hot Rates [hotwire.com] [hotwire.com]
hotels or look for latest promotions here [hotels.com]
Copenhagen Travel Guide [skyscanner.com]