Working for Copenhagen City?
besides being a member of Internations, I work for the Copenhagen City Council (Københavns Kommune).
Each year we post 30 jobs (socalled "integrations- og oplæringsstillinger") aimed at people that have a hard time finding a relevant job here in Denmark, mostly due to a foreign degree and not-so-perfect Danish skills.
The jobs are aimed at both unskilled, skilled and academically schooled people. Most of the jobs have deadlines in first half of June.
The positions are not time restrained and are mostly relevant if you plan to stay here for several years and need a way into the Danish labour market. First year year, you use 20% of your time for training, and get 80% salary, and after the first year it's normal conditions and pay.
Please refer to Protected content where you have further information, and the actual job offers. There's an info page in English, but be aware that the working language in Copenhagen City is Danish, so you do need a starting point in Danish.