From the research I've done, the name 'Gynner' was anglicized from the Norman word for engineer, or the builder of military war machines like trebuchets, and was listed in the Domesday Book as in Ellastone, Staffordshire. In the 1600's, within one generation (in my line) it went from Gynner to Ginder and Genders in different documents.
This Staffordshire family is not to be confused with the Dutch Janders, porcelain makers, who came over with William of Orange. Some of them moved to Birmingham (my ancestors), and some to Manchester, to the same parishes as the Snellsons (a family from the next village over from Ellastone).
There was mention of one Genders in London during the middle ages, I believe, whose name may have fit your French rule of description.