France has a fairly low crime rate, and this is also true for Saint-Tropez. Most of all, you should be wary of street theft and fraud, especially in crowded places. You should also keep an eye on your purse and wallet when buying goods in small stores and hawker stalls.
It is better to exchange currency in the branches of the state bank Banque de France (and the rate is the most favorable, and safe). In emergencies, you should contact police officers in patrol cars. Documents on the streets are usually not checked, but even if it happened, the policeman has no right to take away your passport. Fines for violating public order and traffic rules are quite high.
In France, you should be extremely polite: do not forget to say hello, goodbye and thank every Frenchman with whom you enter into a dialog.