As many period illustrations will attest, French cavalry did not use cartridge boxes, Simon. The following engraving by Parrocel shows a Garde du Corps trooper from behind, and it is quite clear that he doesn't have one :
The illustration slightly post-dates the reign of Louis XIV (it's from the late 1720's or early 1730's) but cavalry accoutrements had remained pretty much unchanged since the 1690's. And Parrocel knew his stuff, having supposedly served as a trooper of horse in 1705 and 1706 (though some dispute he actually did). Being a member of a household unit, our Garde du Corps above boasts a splendidly ornamented bandolier, but finery set aside his accoutrement is otherwise identical to that worn by line cavalry units.
According to Michel Pétard, who wrote and illustrated a book on C18th French military accoutrements, ammunition for the carbine was either carried in small leather pouches sewn to the pistol holsters (and therefore concealed by the cloth housings), or simply kept in a light powder horn attached to the shoulder belt. This may not seem like a lot, but carbines were not supposed to be used much outside of picket and foraging duties. The cavalry were primarily shock troops who used their sword and pistols to punch through the enemy. Firepower wasn't their defining attribute and half a dozen shots was probably more than enough for a trooper to fight a single engagement - especially given the difficulty of reloading muzzle loaders on horseback.
When a powder horn was used, here's how Pétard visualises its position on the belting (in this case that of a horse grenadier, which accounts for the piping on the bandolier), using a period illustration by Delaistre as a basis :
Powder horns could be sophisticated little affairs, complete with dispenser and measuring devices. The rather ingenious model shown below was devised by a Mr De la Chaumette in 1715 and contained both powder and balls, feeding them into the gun barrel through two separate funnels. It was deemed a little too tricky for the hands of clumsy soldiers however, some forgetting to block the influx of powder with their finger or emptying the wholl ball container into the barrel of their gun instead. I have no idea whether it was used in the field, but it's definitely an interesting contraption. It is however most likely that cavalry troopers used more conventional powder horns and kept their bullets in a small separate bag .
One morning I shot an elephant in my pajamas. How he got into my pajamas I'll never know.