Which phrase is the correct one?
to increase competitiveness in the EU labor market
to increase competitiveness on the EU labor market
In is correct.
'On' in terms of a market means something for sale. You put your house 'on the market'.
English is not my forte. But here is my two cents. IN is correct since competitiveness is an event that must occur in a population. In this case the population is the EU labor market
Change the word competitiveness to murderousness and it will be clearer. :)