If I understand correctly, Franco's regime incorporated different groups with a wide range of ideological views - fascists, conservatives, monarchists, the Catholic Church etc. But what were his own views?
Franco's ideology was simple: To attain and hold complete power for as long as possible. Franco was an accidental dictator. The Junta that plotted the overthrow of the Republican government was originally headed by General Jose Sanjurjo, and largely Planned by General Emilio Mola. Sanjurjo, a Monarchist, and Mola, did not envision a lengthy military government. Sanjurjo and Mola wanted to "Clean out the barn", restore order, and hold elections (Wherein only "Nice" screened political parties could participate.) The Junta envisioned that some of the Republican reforms, like the separation of church and state, would be preserved. A coalition of Monarchists, Carlist followers of Fal Conde, Falangist followers of Jose Antonio Primo de Rivera, and conservatives foresaw authoritarian rule, but by elected civilians. And Franco, a national figure in Spain, did not join the conspirators till very late in the game. BUT....On the third day of the Nationalist rising, Sanjurjo was killed in a plane crash. When the Nationalist revolt failed in Barcelona, prominent Nationalist General Manuel Goded Llopis was captured and shot by the Republican Army. A year later, General Mola died when his plane hit the side of mountain in thick fog. Before Franco was chosen by the Junta to be head of state, the most senior General, Miguel Cabanellas warned the other officers: "If you appoint Franco as head of state, he will think that Spain belongs to him, and he will never give up power unless he dies. You do not understand this, but I do, because I have commanded him" Cabanellas was right on the money, because Franco merged the Conservatives, Carlists, and Monarchists and the socially radical Falange Espanola into his homogenized "National Movement", which has no platform or ideology to speak of, except to keep Franco in power. With the death of Mola and Goded, the only two Generals who would stand up to Franco, his position as head of state was secure. And Franco succeeded in his goal of maintaining power for almost forty years.