Besides watching your belongings (which is necessary wherever you are), there is really no reason to feel uncomfortable traveling on the trains and buses in the Cote d'Azur. I travel to the region when my husband attends a convention in Cannes and am often getting around on my own. I'm good with it and very appreciative of the transportation services available in the Cote d'Azur.
Ditto on the St. Tropez boat trip advice given here, but before you travel, be aware that the boat goes to the village of St. Tropez and the beaches are some distance away. This is fine for most travelers, but i'd hate for you to travel expecting that you will arrive at the beaches.