The third F is for "Fátima" (Our Lady of Fátima). And besides the Football, it has nothing to do with Bread and Circus, as every people should cling to their Faith and customs.

Edit: This is present in your own links you didn't bother reading, and you'd see those "Three Fs" wasn't any Regime motto, but post 25 April propaganda, the official one was "Deus, Pátria e Família" (God, Fatherland, Family).