Thanks for pointing me towards this thread Smudwhisk, I have been very busy with another project and unable to answer until now.
I am descended from this line through Jacques Martin, born 1714, son of Jacques Martin and Marie Beaucourt. He described his father as a native of Picardy.
Jacques Martin senior appears twice on the Royal Bounty records 1727-9:
"Jacques Martin, 44, of Picardy, his wife, 43, and 4 children, all under 14 years"
"Jacques Martin, of Abbeville, 46 years, Weaver, his wife and 5 infants, Spitalfields, 16 Pounds, 18 Shillings, 0 Pence"
When his son Essaye Martin, born 1710, died in the French Hospital in 1788 he described himself as the son of Jaques Martin of Amiens in Picardy. When another son Guilluame Martin, born 1718, died in the same charitable institution five years later he described their father as 'Jaques Martin born at Snerpon [i.e Senarpont] in Picardy, who left France for cause of religion'.
So all the sources agree he was from Picardy, though give conflicting places of origin, Amiens, Senarpont and Abbeville. Senarpont is a small village equidistant between the two more major population hubs of Abbeville and Amiens in the Somme district of France. It is not uncommon in the English records for the nearest big town to be supplied, because as you can see the clerks of the French church in England were often from more established second or third generation families and were not always familiar with the smaller locations and their spellings.
I have little doubt that a Magdeleine Martin, born circa 1678 and married to Joseph Terraube in London 1722 was a relative, almost certainly a sibling, as she describes herself on this marriage as a 'Native of Senerpoint [sic] in Picardy, daughter of the late Esaie Martin and Marie Desmarets'. Joseph Terraube stands as godfather to the youngest child of Jacques Martin and Marie Beaucourt, eleven months after his wedding. Her sister Susanne Martin had married at the same church seven years earlier to Daniel Bouy. Daniel also stands as a godfather to a child of Jacques Martin and Marie Beaucourt,in his case a year and a half after his marriage. Susanne was a godmother to an earlier child of theirs.
Susanne was baptised on 15th March 1669 at the Oisemont Protestant Temple, the nearest protestant congregation to Senarpont, as the daughter of Isaye MARTIN and Marie DESMARESTS with godparents Noel MATREL, a gentleman, and Suzanne DEPARIS. The couple had married at the temple on 6th June 1668, and also baptised a son Isaac Martin there in 1671 with godparents Isaac LE GRAND and Magdeleine (Marguerite) BEAURAIN.
The Huguenot churches were not closed or demolished overnight, in fact it was a slow and gradual process from 1661-1685. The majority, something like 80% had already been closed or demolished by the time of the revocation. I believe the Oisemont temple was closed by Royal decree sometime after 1671, (I do have the exact date somewhere). This is why baptisms don't exist there for the couples younger children Magdeleine and Jacques, who from the London records appear to have both been born in the period 1678-1683.
After fleeing to England the family were first members of the Huguenot congregation based in Canterbury, Kent. The father Isaye/Easie Martin was buried there in May 1702. Susanne joined the Threadneedle Street congregation with a testimony of faith from the Canterbury congregation.
