Sometimes I flip to a random entry in my giant Encyclopedia of the Automobile and share it with Oppo. This is one of those times.
R.E.A.C. stood for Recherches et d'Études Automobiles Chérifiennes. The company was based in Champigny-sur-Marne outside of Paris, but the cars were apparently built in Casablanca, Morocco where Ingrid Bergman once asked Sam to play that depressing song. Some Googling leads me to believe they were a racing club in Morocco that used modified Panhards that decided to try manufacturing cars.
The idea was to put a light, fiberglass sports car body on a Panhard Dyna chassis using the Panhard's mechanical stuff which at that time included a 40HP, 850cc two-cylinder powering the front wheels. The fiberglass body ended up weighing less than 200 lbs. so I guess 40 horses was enough. Only 15 cars were built as the whole enterprise proved too expensive, but they're pretty rad looking. Most of them were open bodied, but 3 coupes were built with gullwing doors and an almost round canopy.
I haven't found any current photos of one, so I wonder if any survived.