Can I translate "I sleep in the night" with "je dors la nuit"? That's the Google translation, but my son who learns French at school thinks it might not be correct (and my French is basic). I did not find this sentence on other online resources, although searching for a while. Are there alternative translations?
Yes, 'I sleep in the night' can and likely means 'je dors la nuit'.
But your son might be right : I think the canonical English phrase would be 'I sleep at night', so maybe the English sentence has a different meaning?
To sleep in, to sleep where one is employed (or where one spends the day).
Je dors sur place la nuit.
meaning : I sleep there (sur place) at night.
Or even : to sleep in, to oversleep.
Je fais mes grasses matinées la nuit.
meaning : I sleep in at night (in the case of someone working weird shifts I guess.)
It is a context thing, pick whatever you feel works best in your situation.