The word trishul I think denotes the three points of the shulam. The "tri" in trishulam = is it from Sanskrit or English like trinity.
Etymology of English word three or tri is
From Middle English thre, threo, thrie, thri, from Old English þreō, þriē, þrī, from Proto-Germanic *þrīz, from Proto-Indo-European *tréyes.
As per Western Linguists, PIE or Proto-Indo-European language is common ancestor of all Indo European Languages, including Deva Bhasha or Deva Vani (देव वाणि) संस्कृतम् (Saṃskṛtam). Obviously, those who know about structure of Sanskrit and its semantics will never believe in this PIE theory.
The "tri" in trishulam is from Sanskrit. Later Indo and European languages had taken from Sanskrit.
In sanskrit threee is denoted by Trí (three), त्रीणि - trīṇi , त्रयः - trayaḥ etc.
There are more examples where Latin and Greek words resemble sanskrit
ashta (eight) - octo (Latin)
sarpa (snake) -- serpens (Latin)
pitar (father) -- pater (Latin), pater (Greek)
Here, "tri" is from Sanskrit.
Actually, the prefix "tri-" is not of English origin. It is borrowed from Latin "tri-" and Ancient Greek "τρι-". Latin and Ancient Greek are closely related to Sanskrit, hence the "tri-" in Sanskrit as well.
However, English shares a common ancestor with Latin, Greek and Sanskrit as well, and English "three" is related to all three of the above.