The criminal duo, identified as an Italian man and a French woman, were caught in the act on Saturday as they tried to rob one of their ten or so known victims, who were all retired priests and nuns, RTL radio reported.
According to a judicial source, the couple obtained their home addresses from a directory listing the clergy members in the Var department of southern France.
The man, aged 22, would pretend that he wanted to make a donation before robbing the victims who'd taken out their wallets to receive the gift, the source said.
The couple, who were taken into custody after questioning on the weekend, now face charges of gang robbery.
During the questioning the couple were also found to be carrying several thousands of euros in cash.
Around ten such robberies have been reported in Var over a period of several weeks and 15 outside the department, RTL said.
In another case of a shocking class of victims in France, The Local reported earlier this month how thieves targeted the home of a family that was killed in the Air Algérie plane crash this summer, just hours after the accident.
And last year a French sportsman who became the first quadruple-amputee to swim across the English Channel was left "sad and angry" after his custom-designed wheelchair was stolen by thieves.