This becomes interesting. Oiseau Bleu comes up as Sarolea, with different engines over the years. 1/3 of the way down this page someone is selling one with the 50LW Sachs.
Facebook page may be useful for further information:
I think the bike is only a badged Sarolea, sold by the Thoria cycle shop in Torhout. Your restoration now is a choice of returning it to Thoria or Sarolea colours.