The two preceding posts say pretty much the same thing, but they may be a bit confusing. Maybe a little clarification of terminology will help.
I found a couple of pictures of the St. Louis, one contemporary (in Dr. Anderson's book) and one modern reconstruction (by Bjorn Landstrom, in his 1950s masterpiece The Ship). They agree with each other in practically every respect (probably because Landstrom based his painting on the old engraving in the Anderson book).
In both pictures she has a typical rig for a French/Dutch warship of 1626: three masts, plus a bowsprit with a spritsail topmast. The fore- and mainmasts have three yards apiece: lower yard, topsail yard, and topgallant yard, each with a square-rigged sail set to it. The mizzenmast has the usual lateen-rigged mizzen sail (please note the spelling - no N in the first syllable of "lateen") and a square mizzen topsail.
The mizzen sail (more commonly referred to simply as the "mizzen") is set to the mizzen yard, and is carried inside the lower shrouds. In the pictures its parrel (sometimes spelled "parral," but not "perrel") appears to be located six or eight feet below the mizzen top (the round platform at the head of the lower mast). There are two horizontal ("square") yards on the mizzenmast. The head of the mizzen topsail is secured to the upper of the two yards, the mizzen topsail yard. The lower of the two yards is called the crossjack yard (or crojack yard). During this period the one and only function of the crossjack yard was to spread the foot of the mizzen topsail. The lateen mizzen didn't get in the way of a sail set on the crossjack yard, because there was no such sail in the seventeenth century.
The mizzen yard stays inside the shrouds regardless of which tack the ship is on. When the ship comes about, the yard is topped up, the parrel is slacked off, the sail is brailed up temporarily, and several energetic souls grab hold of the lower end of the yard and carry it bodily around behind the mast to the new lee side. It's a clumsy process, but it does work.
I don't follow Chuckfan's phrase "outside of the hences." Maybe it's a typographical error. I looked up "hence" in several dictionaries, nautical and regular; none of them contains such a word used as a noun. A hance is a "step" carved into a piece of wood as a means of making in narrower. The term appears most frequently in reference to the shape of a rudder; the typical eighteenth-century rudder had two hances (or "hancings") in its after edge. I've also seen it used to refer to the ornamented "steps" in the top of a ship's bulwark. But I don't see what either of those usages has to do with spars or rigging.
A couple of months ago I had an interesting conversation with the gentleman who commands the reconstructed seventeenth-century ships at Jamestown Settlement. He tells me that his crew can accomplish that evolution with the mizzen of the Susan Constant in a minute or two. He also says that handling the lateen mizzen is such a nuisance that, if the program for the day's sailing involves quite a bit of tacking, he doesn't bother to set it in the first place. It should be noted that the Susan is, even by seventeenth-century standards, a small ship, with no mizzen topsail. Heaving the enormous mizzen yard of a ship like the St. Louis around must have been quite an exercise, even for the much larger crew she must have carried.
Sometime after the middle of the nineteenth century, some ships started setting a square-rigged sail on the crossjack yard. That sail was, naturally, referred to as the crossjack. By that time the lateen mizzen had been replaced by the much more practical gaff-rigged (or gaff-and-boom-rigged) spanker (or driver), so the potential collision of the mizzen and crossjack was no longer a problem.
Hope that helps a little. Good luck - and if you want to do a good job of rigging a model like that, consider buying the Anderson book. It's one of the biggest bargains currently available to the ship modeler.