Origin of the Name
MESPLETS.- Mesplez, marquisat du Béarn, érigée en 1732. Dérive de minus, moins, et de platus, plat. Méplat, est une pièce de bois de sciage, plus épais d'un coté que de l'autre.
MESPLETS.- Mesplez, marquisat of Béarn, originated in 1732. Derived from minus, less, and platus, flat. Méplat, is a piece of wood for sawing, more thick at one side than the other. (I picture a wedge).
When I first read this I thought "This isn't anything close to the family story I heard. Maybe the family story is wrong." As time has passed the family story has become more plausible. In fact other than the reference to the marquisat of Béarn I don't believe a word of this definition.
What follows is my best guess at the etymology at this time. I've communicated with native speakers of the area we believe the name originated so I'm fairly confident of this information but as more research is done we may find the etymology is different.
The names Mesplay, Misplay, and Messplay are the common forms in the USA. They are anglicized (spelled to pronounce correctly in english) versions of Mesplais (silent "s") which is the name of a family that lived in the St. Genevieve/Kaskaskia area in the late 1700's and early 1800's. This family originates with Pierre Mesplay who was a voyageur as best we can tell.
I believe Mesplais is a galicized (spelled to pronounce correctly in french) version of the name Mesplet (the "t" is silent, "et" makes the "ay" sound). This is conjecture since we haven't made a direct link between Mesplais and Mesplet yet. Mesplet is the name of a man who lived in Louisiana in the early 1700's. Sieur Mesplet was documented as coming from Pau in Béarn (south of France near Lourdes). Mesplets seemed to be involved in trapping, scouting, and trading. There is also a Fleury Mesplet who formed Montreal's first newspaper - the Montreal Gazette who is supposed to be descendant from the marquisat of Béarn. Pierre Mesplay is listed in a census as coming from Canada.
Mesplé is the common form of the name found in France. Mesplez and Mespoulet are other less common forms. Note that the "z" and "t" are silent indicating the sound "ay" as does "é". I believe all these to be other galicized versions of the original name. The Mesplé name can also be found in the USA and Canada. When found in the USA it seems to indicate a family that emigrated at a later date than the Mesplays. It may be that there being more literacy at this later date allowed them to keep the spelling that the family used while in France.
The original name seems to be something close to Mesplet or Mespolet. In this case the original language would be Occitan which was a common language in the Middle Ages in the South of France and still in use in some parts of that area. In Gascon Occitan, mesplèr means medlar tree and is derived from the Latin mespilus germanicus. Note that the "è" makes the "eh" sound as in "sent" and the "r" is silent. The medlar is called a nèfle in french which is why I don't believe french to be the original language of the name. The fruit of the medlar tree is called mespla or mespola in some Occitan dialects. The "a" sounds like "o" in "hot" and the "o" sounds like the "oo" in "look". Mesplet/Mespolet (pronounced mess'-play/mess'-poo-lay) are the diminutive forms of mespla/mespola and therefore mean "little medlar fruit".
This matches very well with the current pronunciations in use and the family story I had always heard. If it were the middle ages and I spoke Gascon Occitan and found some children under a medlar tree I might just call them little medlar fruit (Mesplet).
I have also read that in an Indo-European language, mesple is derived from "mes" (full) and "ple" (moon). How this relates I'm not sure but the medlar fruit could be described as a "full moon".