Precisely - "international" is an attributive adjective in this case - remove it and you still have the copular phrase "I am a man". Remove "international" from "the man is international" and you don't have a sentence.
In English, a predicative adjective comes after the verb - "I am hot", "he is strong", "the box looks heavy", "the milk tastes sour", whereas an attributive adjective typically comes before the noun that it qualifies ("hot" in "I drink hot tea" is an attributive adjective, even though it comes after the verb). In Irish, because the verb comes before the noun that is qualified by an adjective, all adjectives come after the verb, and you need to interpret the whole sentence to decide whether an adjective is attributive or predicative, and what mutations should apply.
tá an bhean bhocht ag teacht - "the poor woman is coming" - attributive
tá an bhean bocht - "the woman is poor" - predicative.