On 31 January 1956, Mbida was both appointed to the Law and Justice Commission and to the Commission of overseas territories of the French National Assembly. He also belonged to the Commission mandated to reform the Title VIII of the French Constitution, on the French Union dated 27 October 1947. In addition, he is designated to serve on the Supreme Labour Council and the Steering Committee of the Investment Fund for Economic and Social Development (), that is a former government agency of colonial-area France, which was established to finance and co-ordinate the provision of facilities for the French colonial territories. His election was confirmed on 14 February 1956 and he immediately joined the SFIO Socialist Group at the French National Assembly and worked alongside Gaston Defferre, Gérard Jaquet and Pierre Messmer who draft the Loi Cadre (1956 Overseas Reform Act) on the autonomy of French colonial territories and the UN trust territories under French administration in Sub-Saharan Africa.