Translations of the terms in ordbogen.com:

fri proces:
(procesret)
free legal representation, free legal aid

retshjælp:
se også fri proces
1.
[free] legal aid
2.
(proc.r.)
legal aid services
3.
(rettens hjælp mod ubillighed)
relief
(ubøj.)
4.
(international ret)
legal assistance

I've widened the term of legal expenses as an insurance term (A Lyng Svensson: Samfundslitteraturs Økonomiske Ordbog retshjælpsforsikring: legal expenses insurance ?) to (legal) costs to subsume court fees in Anglo-Irish parlance:

...'Sometimes you may hear the word ‘costs’ being used loosely to mean the entire cost of bringing or defending a case – including the amount any solicitors charge for their work, the cost of any expert or medical reports, as well as any *court fees*.'

'...Hvis du får fri proces, betaler statskassen blandt andet salæret til din advokat og nødvendige udgifter forbundet med *sagens behandling eller oplysning*. ..'

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Note added at 1 day 1 hr (2023-12-06 11:07:40 GMT)
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PS in the UK, legal aid comprises free legal advice (previously, the first half-an-hour of a Solicitor's time on the Legal Aid 'Green Form Scheme') and representation, so IMO the other way round from the first answer.