Learn French: Ils m'agacent, ces conducteurs impatients. - They annoy me, these impatient drivers.

This is a perfect example of right dislocation, a very common way to structure sentences in conversational French. By using the pronoun Ils right away, the speaker gets straight to the emotional reaction (m'agacent), and then tags the actual subject (ces conducteurs impatients) at the end to clarify exactly who they are talking about.

Would it be grammatically correct to just say Ces conducteurs impatients m'agacent?

Yes, absolutely! That is the standard, neutral way to structure the sentence, and it is exactly what you would see in formal writing. The right-dislocated version shown here is simply a more spoken, expressive way to emphasize the topic.

Is the pronoun m' here a direct or an indirect object?

It is a direct object. The verb agacer (to annoy or irritate) takes a direct object in French, meaning you annoy someone, not to someone. The pronoun me drops its e because agacent starts with a vowel.

Why does the adjective impatients come after the noun here?

Most adjectives in French follow the noun, especially those describing a mood, behavior, or personality trait. Only a specific group of common, short adjectives (often remembered by the acronym BANGS: Beauty, Age, Number, Goodness, Size) typically come before the noun.