Jour et nuit
This literally translates to "day and night" but conveys the meaning of "all day and all night" very well.
You can also say:
* 24 heures sur 24 (24 hours out of 24) - This is more literal and emphasizes the constant nature.
* Tout le temps (all the time) - This is a more general way to say it, but still conveys the same meaning.
The best option will depend on the context and the desired level of formality.