We do not know whether he was born in England or on the Continent. England had a substantial émigré population, and the surname Vial was not uncommon in the west country. The French Episcopal Church in Plymouth, Devon recorded the baptism on 17 April 1754 of Pierre Vial, son of Joseph Vial and his wife Marie, born 25 March 1754. The same church also recorded the baptism of Joseph Viall, born 10 October 1737 and baptized on 30 October. However, the date of Pierre's baptism is inconsistent with the marriage of Peter de Vial and Mary Tremlett in 1764. The fact that de Vial's widow and daughter travelled to St. Etienne during the Peace of Amiens in 1801 led St. Clair to suggest that Peter de Vial may have had connections with the armaments merchants of that city.There is a record of Peter de Vial, merchant of Exeter, paying duty for the indenture of an apprentice, William Colson, on 6 January 1772.
Around the time Catherine Oak gave birth to Charlotte in 1777, Mary Tremlett had been dead for several years and Peter de Vial was declaring bankruptcy. If the earlier birthdate of 1766 for Mary Jane is correct (her tombstone records she was 75 when she died in 1841), then 1777 would also have been when she left England at the age of 11 (as she claimed) to find her relatives on the Continent. Perhaps her father’s relationship with Catherine Oak, and the birth of an illegitimate sister, prompted Mary Jane decision to search out her family.
Peter de Vial obtained his certificate (i.e. discharged his bankruptcy) in February 1778. In the London Gazette notice he was described as a “Merchant, Dealer and Chapman”, a somewhat less solidly respectable status than the burghers and property owners in Mary Tremlett’s family. Moreover, de Vial is identified as being “of the Parish of St. Thomas the Apostle”, which could imply that his roots were more in England than France or Switzerland.
We cannot ignore the possibility that Mary Jane’s claim to have gone to France as a girl, and to have lived with wealthy relatives, was another lie intended to improve on what may well have been the unglamorous truth of her early life. I am not aware of any independent evidence of her residence in France. However, there is an extant record of the indenture of a Mary de Vial of Exeter to Elizabeth Ann Broadmead, milliner, in July 1782, just after Peter de Vial married Catherine Oak.
Later, the 1791 Deed of lease and release of the inn in Exeter inherited from Mary Tremlett’s family describes Mary Jane and Sophia as spinsters of Barnstaple.
No evidence has emerged so far to establish the existence of a brother in Cadiz. One possibility is that Peter de Vial had a son from a previous relationship (we do not know how old de Vial was when he died): another is that he himself had a brother in business in that city. Alternately, the brother may have been a confabulation of Mary Jane’s, intended to suggest a familial connection to the highly placed Spanish branch of the de Vial lineage.
Other children were born to Peter de Vial and Catherine Oak after their marriage. A son, Peter John Claud de Vial, was baptized on 22 March 1788 at St. Thomas the Apostle’s, Exeter. It is probable that he died in infancy, as another son, Peter, was baptized in the same church on 28 May 1791, at the same time as a daughter, Julian Catherine. The England Deaths and Burials 1538-1991  index also includes the deaths in Devon of a John de Vial and a Catherine Devial, both with a father named Peter, in February 1785 and December 1790 respectively.
The sister Mary Jane later wrote of having visited in Lynmouth in 1813 may not have been a fantasy, although no further records of Julian Catherine de Vial have come to light so far. If she survived past infancy, she possibly went to France with her mother and Charlotte in 1801. A Peter de Vial, merchant, of 10 Dalby Terrace [Islington], is mentioned in the House of Commons Papers for 1837 (Vol. 48, p.xxiv) as subscribing 3,000 pounds for 60 shares in Westminster Bridge, Deptford and Greenwich Railway. Peter de Vial the father was again bankrupt by 1789 (London Gazette, Nov 28 1789, reproduced in The Times). He is thought to have died in 1791 (St. Clair, p.252).
 UK, Register of Duties Paid for Apprentices' Indentures, 1710-1811
 Gentleman’s Magazine and Historical Chronicle, Vol.47, p.556
 England Deaths and Burials 1538-1991