Chicken/pullet seems to have gone the opposite way: pullet (French) is exclusively for the animal but chicken (Germanic) can be either the animal or its meat.
Is chicken really German though? A hen is called "Huhn" (Das Huhn), and chicken may be more appropriately translated as "Geflügel" (or rather, the latter would be poultry; chicken would be "Huhn" or "Hähnchen"). I don't see the germanic origin insinuated here for the word "chicken", whereas I do so it for "hen" <- "Huhn" quite easily. (And "Geflügel" has "Flügel" which relates more easily to flight/to fly, or better Flügel=wing).
Funnily enough in Switzerland they use "Poulet" to mean exclusively chicken meat.