The two words are synonymous, and either phrasing could be used, although Google's Ngram tool shows that social issues seems to be the predominant term.
I wouldn't go so far as to say the two words are always interchangeable. At least in the U.S., students go to college majoring in social work, not societal work. In the context of social issues, though, social issues may be more common, but that doesn't mean it's always more correct.
Perhaps a good follow-on to your question would be: When might one be preferable over the other? I think social would almost always be a safe bet, but I can think of one reason societal might be preferred in some contexts – a narrower definition. According to NOAD, societal means:
societal (adj.) of or relating to society or social relations : societal change.
The word social has pretty much the exact same meaning, although its meaning does seem to be subtly broader:
social (adj.) of or relating to society or its organization : a major social problem | a traditional Japanese social structure.
• of or relating to rank and status in society : a recent analysis of social class in Britain
• needing companionship and therefore best suited to living in communities : we are social beings as well as individuals
One "Writing Tips" website says that the two are pretty much synonymous, although societal might sound more pompous outside of a formal academic setting:
societal appeared in the latter part of the nineteenth century as a more serious, scholarly alternative. It is mostly seen in such usage and is otherwise considered pretentious.
The question was also asked on ELU a few years ago; I think Neil Coffey's comment there sums it up pretty well:
if there's any confusion, "societal" allows you to disambiguate – it is probably for this reason that it is reasonably common in academic writing.
Imagine you were organizing a conference, and you were considering two titles:
- International Conference on Societal Change
- International Conference on Social Change
The latter title would work if the conference intended to address issues like poverty, unemployment, or substance abuse. The former seems to have a more narrow focus; specifically, a more academic view on how society is evolving.
Then again, maybe I'm just reading too much into it.
Back to your original question:
I am trying to translate the French phrase questions de société. We use it when we speak of issues broader than just social issues (workers, unemployment, poverty...). Questions de société also includes issues about evolution of society, cultural identity...
English works pretty much the same way. Social issues may often refer to broader problems like unemployment and poverty, as well as cultural identity, while societal issues can also apply to both. However, the surrounding context (such as the title of a conference) might create an initial impression in one direction or another.