PERIDOT: THREE AGAINST THE MOB by Tyree Campbell

Who is Peridot?

She’s a young American woman named Ricia Ryder, stranded in France, and she has more problems than any superheroine should have to deal with.
On a tour of southern France, Ricia was robbed of her papers and her money, and was compelled to live off the grid. An ancient Celtic goddess gave Ricia succor and superpowers. Eventually Ricia took up with a young woman reporter who subtly hits on her—thus far without success—and whose job it is to expose Peridot’s activities to France’s viewing audience. Ricia herself is attracted to a gendarme who would arrest her immediately for violation of the National Treasures and Antiquities laws, should he learn that she sells precious French artifacts under the table. She’s been tasked with helping people, and with fulfilling a mysterious agenda whose end game could well result in the torture and deaths of those around her.

. . . and the goddess who empowered her to become Peridot is insane!
 
In the Peridot series:
Peridot-Three Against the Mob
Peridot - The Caesar Talisman
Peridot - Avatar
Peridot - Balance of Power