FOIX, an arrondissement in the department of Arriège, in France, extending over 803 square miles. It is divided into eight cantons and 104 communes, inhabited by 78,280 individuals. The chief place, which gives name to the circle, is situated in a wide and fruitful valley, on the left bank of the Arriège. It is old and ill built, has some trade in hats, stockings, and caps, and contains 3600 inhabitants. Long. 1. 30. E. Lat. 43. 2. N.