Nicolas-Joseph Wackenthaler (1830-1913) came from a family of organists in Alsace. He was organist at St George's church in Sélestat, and taught in Paris, though later moved to Dijon where he became organist at the cathedral.
"L'Adoration des Bergers", subtitled "Fantaisie pastorale pour les fêtes de Noël", is, frankly, a fairly trivial piece and is, I suspect, more or less typical of his output given that he was apparently held in more esteem as a performer and teacher than as a composer.
It's in three parts: "L'arrivé des bergers" (the shepherds' arrival), "L'adoration des bergers" (the shepherds' adoration, the Adeste Fideles section) and "Le retour des bergers" (the shepherds' return - an almost exact reprise of the arrival).