Well, according to a surname database, it is most predominantly used in Argentina, Spain, and Uruguay. There seems to be only one bearer in Switzerland, so I doubt it's Swiss or French (you mentioned seeing it in the eastern, French speaking region of Switzerland). I'm not yet sure about the meaning, but I'm guessing it is of Spanish origin due to the concentration of bearers in Latin/South America and Spain.
It also seems to be spelled as "Esmorís", and according to a disgambugation page on the Galician Wikipedia, it is a topographic (meaning that it relates to an area or region) surname referring to one of several locations named "Esmorís". I'm not yet sure about the etymological meaning, however, as all the "Esmorís" pages seem to be pretty empty/undeveloped.
Also unlikely, but the name could be related to "Esmoriz", the name of a city in Portugal. I doubt this considering Argentina, Spain, and Uruguay do not speak Portuguese.