What’s the translation of the following:

Question

Magno Gaudio Christiani Doctrinas Christi audimus.

Is it: We, the Christians, hear the teachings of Christ with great joy.

Or the audimus is an error?

Answer 1

Yes, that's an accurate translation.

I presume that your source of confusion is the fact that there seem to be two subjects: (1) an implied first-person plural "we" from audimus, and (2) Christiani, which would seem to require a third-person plural verb.

The trick here is to realize that a noun can be placed in apposition with an (understood or explicit) pronoun.

Here is a famous example from Cicero's First Cataline Oration that uses an explicit pronoun with a noun in apposition:

Nos autem fortes viri satis facere rei publicae videmur, si istius furorem ac tela vitamus.

Translation:

But we, brave men [that we are], seem to do enough for the republic if we avoid his wrath and weapons.

The same thing is happening in your quote, except that the nos is implied. My only suggestion, for idiomatic English, would be to say, "We Christians" instead of "We, the Christians."