A Google search reveals only nine results. All of them are pages that list the title of this act. The Parliamentary Archives website lists the act's description as, "An Act for naturalizing Louis Sechehaye, George Frideric [Frederick] Handel, Anthony Fursteneau and Michael Schlegel. [Handel's Naturalisation Act]".
The somewhat boring answer to this is: no one in particular. Or, at least, not necessarily so.
Naturalisation always required an act of Parliament.
Edited to add, that in summary of my posts below, and to specifically answer the original question, Louis/Lewis Sechehay(e) was:
A barber-surgeon who had immigrated to London in or before 1718 from perhaps Metz, Liège, or Cologne (or some other city entirely). One explanation of his origins might be that he was from a Huguenot family that had emigrated out of France to elsewhere, and then about a generation later, he went to London (not a unique trajectory).
Then in 1718 he married a woman named Patience Blake (who was likely a native, since she did not have to be naturalised, and has a rather typical English name). The couple had at least three children in London: Richard (1721), John (1722), Mary (1724).
In 1722 Louis, as a landowner (not necessarily of great means), was made to take the Oaths of Allegiance, Supremacy, and Abjuration before the City of London pursuant to the Papists Act 1722 (refusal could lead to seizure of estates). And indeed he also appears in some Land Tax records.
Then in 1727 Louis petitioned Parliament to be naturalised as a British subject. Handel made the same petition a short time thereafter and his name was attached to Louis's petition (as was the usual practice), alongside two further petitioners, before a committee of members of the House of Lords considered their petitions. All four were granted their requests.
Sechehaye was buried in London in 1745.