I found that they are kind of Francophiles in Copenhagen: fashion, food and wine from France were featured pretty much everywhere.
We did get probably one of the most amazingly good pulled pork sandwiches I've ever had anywhere from a French restaurant at a street fair. Incongruous, I know, but the results were spectacular.
I would highly recommend seeing the David Collection over by Rosenborg Palace. It's a very well-curated private museum with a lot of mesmerizing examples of Islamic art.
We had a nice stroll around Fredriksburg Gardens, and lo, somehow ended up at the Carlsberg brewery.
They keep a stable full of giant Jutland horses for parades and public appearances. Not quite as fancy or flashy as the Clydesdales, but they were solid blocks of muscle on squat frames.
You can tour the brewery, or just hang out in the beer garden. The food was actually decent, but it was so windy you ended up wearing it if you weren't careful.