The Le Campagnard, Gaston, and Pernet Mugnier Christian brands are being recalled following the detection of Brucella in unpasteurised milk used in production.
The FSA acted after French authorities issued an alert about potential contamination in certain brands of the reblochon cheese.
The affected cheeses were not supplied to any UK businesses but the industry body is warning people who may have bought the cheese in France, not to consume it.
The packs were sold from February to April this year in 450g packs.
Brucellosis infection occurs through contact with infected animals or consuming unpasteurised (raw) milk or dairy products.