French Grenadiers

As far as I know the Grenadier was a French innovation - it started with the Du Roi Regiment who had 4 per company in 1667 at the instigation of the famous Colonel Jean Martinet. The experiment was successful and in 1670 they were grouped into a company. The Anjou, Lyonnais, Dauphin and Royal Vaisseuax followed in early 1671. Flintlock muskets were carried from 1670. The sling - the Grenadiere did not become universal until the early 18th century.

Grenadiers a Cheval
Louis XIV, in 1676, created a company of horse grenadiers recruited from the cavalry and armed with a musket, pistol and sword. This company was attached to the Maison du Roi (king's household). Their motto was "Undique terror, undique lethum".

"L'art militaire ou Les Exercices de Mars, livre à dessiner", de Nicolas Guérard, Paris, chez N. Guérard, s.d. [vers 1695]