The most serious safety concern on a Nice beach is likely to be the sun. There are no biting insects and the water harbours few hidden dangers except for jellyfish which are endemic in the Mediterranean and can be a serious problem. See more.
The baie des anges is not beset by strong and invisible currents. What you see is what you get. If winds are whipping up the sea and it looks agitated and dangerous, it is.
When in doubt, pay attention to the flags that fly from the beaches between May and September. There are five flags: a blue flag means clean water; a yellow flag means that the water quality makes bathing inadvisable; a green flag means that sea conditions are safe; an orange flag means that swimming is dangerous either because of an agitated sea, currents, jellyfish or other condition; a red flag means that swimming is forbidden. All beaches with lifeguards and first-aid stations fly flags.
On public beaches, there are lifeguards on duty daily from 9am to 6.30pm from mid-June through mid-September. Three public beaches also have lifeguards on weekends from mid-May to mid-June. All private beach-restaurants have lifeguards on duty daily from mid-May to September. You can tell that lifeguards are on duty on a public beach if there are flags flying. Otherwise, see this list of public beaches with lifeguards and a first-aid station:
There's also a special boat that patrols the Baie des Anges ready to assist swimmers in trouble.