It may be because of the intent behind the sentence. In French, he's introducing his wife as his spouse; it's understood as a respectful introduction. In English, using the phrase "his woman" would be very disrespectful and offensive. So while the words match, the intention behind the sentences do not.
Grammatically, "sa" may indeed be either "his" or "her". However, the French sentence will be understood with "sa" as relating back to the subject of the sentence, « il », i.e., "his wife". If you want to way "her wife", you would say "Il présente sa femme à elle (or the name of the other person).
The sentence here is using the verb "présenter".
3rd person singular of the verb in the present tense is "présente" so it is "il/elle présente" as appropriate. The spelling does not change.
If it was the adjective rather than the verb then the spelling would change depending on the gender of the noun giving masculine "présent" and feminine "présente".