Probably not. They were almost certainly English citizens, born in England, and members of the Church of England.
It was more than 250 years after John Witt’s arrival in Virginia that the Huguenot legend first surfaced. The claim that the Witts were Huguenots was first made in print in 1924 in a publication called Year Book No. 1 by the Huguenot Society of the Founders of Manakin in the Colony of Virginia. No evidence was offered other than the proximity of the brothers John and William Witt to the Huguenot settlement at Manakin. It was repeated in 1927 in Virginia Soldiers of 1776.
The founder of this Huguenot Society, Mary Latham Norton, was a descendant of William Witt who apparently assumed that William Witt was a Huguenot and an otherwise undocumented settler of the Manakin settlement. She relentlessly promoted that view in the society’s documents and in a number of other publications. She was, however, unaware of the Witt records in Henrico and Charles City County and thus did not realize that John Witt of Charles City County was the immigrant and that his sons were born in Virginia. Nonetheless, the Huguenot Society persisted until quite recently in listing “Jean” and “Guillaume” Witt among the “authenticated founders” of the Manakin settlement, claiming that they arrived in Virginia about 1700 from France. Although the Huguenot Society has abandoned this stance it remains a very difficult myth to dispel, despite the fact that there is not a shred of evidence to support it.
Indeed there is a mountain of evidence to dispel this myth. We know that the Witt brothers were from Charles City County, that they were children of an English citizen, signed their own names as “John” and “William”, and never appear in a single record of the Manakin settlement. Nor is either included among the many Huguenots who were naturalized as British citizens. They merely found themselves living, along with many other Englishmen, in the same county as the Huguenot settlement. At least one third-generation Witt did indeed marry a child of Huguenot immigrants, but that simply reflects the assimilation of Huguenot descendants into the local population.
Furthermore, while there are several 19th century accounts of prominent Witts, not a single one lays claim to Huguenot ancestry.
The settlement at Manakin was in King William Parish, a French-speaking parish established specifically for the benefit of the Huguenots inside the boundaries of St. James Parish. Its vestry book records births, deaths and other information for the Huguenot families in the area of Manakin, including those who resided outside the Manakin settlement. No Witt appears at all in those records during the first thirty years, except for a notation of the birth of a child to Benjamin Witt, who had married the daughter of a Huguenot immigrant. A few years later John Witt III appears as a taxable within the parish for the brief period in which he lived in the southern reaches of the parish, but so too do many other non-Huguenots. The parish, which had no fixed boundaries, expanded its geography over the years as its French members expanded outward from the original settlement, thus encompassing several non-Huguenot residents.
The later discovery of the marriage of John Witt and Ann Daux seemed to some researchers to support the French connection. As noted elsewhere, the Daux family was probably were English as well.
The final nail in this coffin is the fact that, until 1680, immigrants not born in Virginia or England required an act of the House of Burgesses to achieve citizenship. Unless naturalized, a foreign-born settler could not own land. These acts listing naturalizations are perfectly preserved, and no Witt appears in them. This despite the fact that we know John Witt was entrenched in Virginia by 1670. After 1680, the governor himself could bestow citizenship, and those records are mostly lost (though the declaration naturalizing the Manakin settlers does exist). Thus, assuming that the brothers John and William Witt were children of the immigrant John Witt, it seems quite likely that they were English.
The name “Witt” in various forms is found among many 17th century English records. It is, of course, possible that these Witts were Huguenots who had immigrated to England a generation or two earlier – though this seems unlikely.
 An 1860 account by Rev. Daniel Witt mentions that he was descended from Huguenots on his “father’s side” of the family. That seemingly refers to his paternal grandmother, who was indeed a Huguenot descendant.