It is a standard English word, do not make it italic.

From the OED:

coterie |ˈkōtərē; ˌkōtəˈrē|
noun ( pl. -ries)
a small group of people with shared interests or tastes, esp. one that is exclusive of other people : a coterie of friends and advisers.
ORIGIN early 18th cent.: from French, earlier denoting an association of tenants, based on Middle Low German kote ‘cote.’

English dictionaries mark words still considered foreign with something that specifically says "foreign". Look in the pronunciation guide to see if there is a symbol for it; usually it's a double dagger.

There is a certain amount of personal preference as to whether a term has been fully assimilated into English. For instance, my 1984 Webster's New World Dictionary marks "voilà" as foreign but not "raison d'etre", and your dictionary may differ. Going by the origin alone is not enough if you don't know the word, as then you could end up italicizing such English words as "inaugural".