For sure, there never has been a Koehler-Escoffier 500 cc monocylinder engine. From the beginning they started with a V-twin engine.

On the forum a member, Ken Lee thought it may be a German "Fafnir" engine as its seems to be alike, but personally I'm almost sure that it's a Swiss Motosacoche 500 cc monocylinder engine. I have to take a look in my documentation about the brand Motosacoche.