"I didn't hear her arrive" would be L'ho sentita.
This happens because past participle has to agree in gender and number with the direct object preceding the verb avere.
The Present Tense in this sentence is correct and not awkward. Both Present Tense and Simple Past tenses are correct here, only context can determine which one to use. Also, notice that US speakers tend to use Simple Past in some contexts where UK speakers would use Perfect Tense.
(American) I don't know the exact grammatical reason, but I will try to see if I can explain it.
When we say something about observing someone else's behavior, we leave off the "to". They don't "to verb", they just "verb".
So we don't "hear him to arrive", we "hear him arrive". We don't "see her to dance", we "see her dance". We don't "feel it (the ground) to shake", we "feel it shake".
Hope that helps.
Because an infinitive verb preceded by a verb of sense (to see, to watch, to hear, to feel) has no "to" in English. Reference: https://dictionary.cambridge.org/us/grammar/british-grammar/verb-patterns/hear-see-etc-object-infinitive-or-ing