French word surface comes from French face, French surmonter

Detailed word origin of surface

Dictionary entry	Language	Definition
face	French (fra)	Face (anatomy). Face (geometry). Head (of a coin). Surface, side.
surmonter	French (fra)	(transitive) to overcome, to surmount, to get over. (transitive) to top, to crown (a building, etc.).
surface	French (fra)	Surface.