"They heard someone shoot."
Translation:Ils ont entendu quelqu'un tirer.
Why is tirer in the infinituve form here please, rather than "shooting" or "they heard that someone had shot"?
Because it follows another verb - entendre - conjugated in the passé composé. Whenever one verb follows another in a single statement (ie without a conjunction) the first may be conjugated but the second (and subsequent) verbs must stay in the infinitive.