What is relation with Elfe - Automobiles Defrance Freres from Vierzon or Eugene MAUVE?
From what I can gather:
Ateliers Defrance FrèresFounded by Eugène Mauve circa 1919
Produced "Elfe" cyclecars
Anzani V-twin engines (703 cc or 984 cc)
Cyclecars MauveFounded by Eugène Mauve circa 1922
Produced "Mauve" cyclecars
Anzani 4 cylinder engines (1086 cc), later NOVA 4 cylinder engines (950 cc)
Société Nouvelle des Automobiles DefranceActive 1922-23
Produced "Defrance" cyclecars
S.C.A.P. 4 cylinder engines (893 cc)
It seems Mauve left Ateliers Defrance Frères in 1922 to create Cyclecars Mauve. It is not clear to me whether the later Defrance was a new creation by Mauve, a new/continued effort on the part of Ateliers Defrance Frères (without Mauve), or an entirely new and unrelated venture. Based on the name and location, however, I think it is likely related to the other automakers in some way.