This is one I have had sitting around for quite some time and have not uploaded for some reason. I have depicted the simpler central cartouche from the 1757 MS; some illustrations show palm leaves round that cartouche. It seems there were no colonels' flags, only the Ordonnance flags; the 1757 MS illustration shows only Ordonnance flags, for instance.
At the Peace of Aix-la-Chapelle in 1748 53 French infantry battalions were disbanded but it was decided to retain their compagnies d'élite as a corps called the Grenadiers de France. Organised in 4 brigades (= battalions) of 12 companies and numbered 40th in rank, the Grenadiers de France and Grenadiers Royaux had 8 battalions at Minden: "as fierce and terrible-looking fellows as I ever saw", said one British eye witness. At Wilhelmstahl 635 were taken prisoner by the 5th Foot and tradition has it that the 5th took their bearskin caps into wear.
Having only a short existence meant that the Grenadiers de France's campaigns were all in the Seven Years War, although they were often in reserve and did not see action.
They fought at or were present at:
1757: Hastenbeck, Hanover;
1758: Krefeld, Bork, Froweiler, Münster;
1759: Minden (Todtenhausen);
1760: Homberg, Sakenhausen, Göttingen;
1761: Duderstadt (Heiligenstadt), Villingshausen;
1762: Grebenstein (Kassel), Johannisberg.
Minden was their most famous action and there they suffered severe losses, mostly from the Allied artillery fire. Much more detail of their history etc. can be found on the Kronoskaf web page and in this account (in French): http://grenadiers-de-france.e-monsite.com/pages/historique-du-corps-des-grenadiers-de-france.html
And this was the uniform in the SYW: