A 1967 article in the British Medical Journal ¹ indicates that this often misattributed quote may have originated in the 1909 book Gayetez d’Esculape ². The book includes italicized quotes followed by comments. "His role is to heal sometimes, relieve often, and console always" was a comment on the 15th century quote "the presence of a physician is very beneficial."
English translation of full paragraph in which quote appears:
The physician is the fiddler of the body and soul. —
He acts on the physical and moral. In the 15th century,
it was said: the presence of a physician is very beneficial. —
His role is to heal sometimes, relieve often, and console always.
Untranslated French version:
Le Médecin est le ménétrier du corps et de l’âme. —
Il agit sur le physique et le moral. Au XV ᵉ siècle, on
disait : la présence d’un Médecin profite beaucoup. —
Son rôle est de guérir quelquefois, soulager souvent
et consoler toujours.
Original paragraph, scanned from Gayetez d’Esculape:
An appropriate attribution line for the quote would be Gayetez d’Esculape, 1909.