"He is making an appeal to us."
Translation:Il fait appel à nous.
I'll say it's idiomatic. To be honest however, that English sentence does not sound particularly natural to me - not a native speaker though.
Il fait appel à nous is to be understood as "he turns to us for help" or something like that
"faire un appel" is a sound phrase, but in a very specific sports context. In soccer for example, when a player runs in towards a favorable position to receive the ball while a teammate has it, he is said to "faire un appel". I am not aware of any other use out of that context.