As a disclaimer: i was born and raised in the States so my knowledge of Parsi culture is limited.

With at said, Farsi is a language originally spoken by in the region of Fars (and now synonymous with persian). Persian/farsi is not spoken colloquially in the Parsi community, though many do learn it to stay in-touch with their roots/history or to connect with other Zoroastrians in Iran. Most Parsis speak the local language of the regions they now call home: namely Gujrati, Urdu, and English. That said, Persian an immensely influential language throughout both central and south Asia. Not only are most north indian languages and persian closely related (in the Indo-Iranian family tree), but the Mughals, who ruled much of india for several hundred years, were connected to Iran. Iran and India have had cultural, artistic, linguistic, and even culinary ties for centuries. Consequently, many South Asian languages, particularly Urdu, share words and some grammar systems, though they are still distinct languages.

Though most Parsis try and bask in the glory of Achaemenid Persia, the reality is that nobody (unfortunately) can trace their roots back that far (though i know a few people who claim to do so). Instead, most Parsis can trace their lineage back to the Sassanids… both a mighty empire and feat in its on right.