The reason why student debt is basically unheard of in Denmark since college is free (although to make that happen, the Danish government poses high taxation towards citizens like they do in order to maintain stable social security nets like subsidised healthcare and public housing, also why they have less homelessness).
Mainly Danish, Swiss and European citizens are eligible to study without stressing over student debt upon graduation. It stems from this: Danish government is more on for the people while American government is more on caring about themselves plus nepotism on the side (MORE & HIGHER TAXES TOO ON TOP OF THAT).
Does the EU have free college and access across the union?
This is not mandated at EU level afaik. Though I found this compare page. Though I’m not sure, what these number include. For example germany is listed as free, though you pay I think between 300 and 400€ per semester. Though that includes a public transport ticket for all of germany (Deutschlandticket). And of course no housing included.