According to Wikipedia, Le Romain du Roi was first used in Médailles sur les principaux événements du règne de Louis le Grand.
A copy of this work is available from archive.org (https://archive.org/details/medaillessurlesp00acad/page/n13)
but the type in that volume doesn’t look like le Romain du Roi to me. However, the date and publisher appear to be correct, and Simmoneau is credited.
Did this type undergo several incarnations? Or is the Wikipedia article simply wrong? Or are my eyes simply broken?