The Catholic Church's stance on fascism was published in March of 1937 via the encyclical Mit Brennender Sorge. This document from Pope Pius XI outlines the Church's objections to fascism, largely surrounding fascism's claim that the State was the final authority. Instead, the Church asserts that there is a different heirarchy. From paragraph 8,

Whoever exalts race, or the people, or the State, or a particular form of State, or the depositories of power, or any other fundamental value of the human community - however necessary and honorable be their function in worldly things - whoever raises these notions above their standard value and divinizes them to an idolatrous level, distorts and perverts an order of the world planned and created by God; he is far from the true faith in God and from the concept of life which that faith upholds

The solution, according to Pius XI, was a particular kind of heroism--via allegiance to the Church and its teachings. From paragraph 21,

In your country, Venerable Brethren, voices are swelling into a chorus urging people to leave the Church, and among the leaders there is more than one whose official position is intended to create the impression that this infidelity to Christ the King constitutes a signal and meritorious act of loyalty to the modern State. Secret and open measures of intimidation, the threat of economic and civic disabilities, bear on the loyalty of certain classes of Catholic functionaries, a pressure which violates every human right and dignity. Our wholehearted paternal sympathy goes out to those who must pay so dearly for their loyalty to Christ and the Church; but directly the highest interests are at stake, with the alternative of spiritual loss, there is but one alternative left, that of heroism. If the oppressor offers one the Judas bargain of apostasy he can only, at the cost of every worldly sacrifice, answer with Our Lord: "Begone, Satan! For it is written: The Lord thy God shalt thou adore, and Him only shalt thou serve" (Matt. iv. 10). And turning to the Church, he shall say: "Thou, my mother since my infancy, the solace of my life and advocate at my death, may my tongue cleave to my palate if, yielding to worldly promises or threats, I betray the vows of my baptism." As to those who imagine that they can reconcile exterior infidelity to one and the same Church, let them hear Our Lord's warning: - "He that shall deny me before men shall be denied before the angels of God" (Luke xii. 9).

And from paragraph 29,

No coercive power of the State, no purely human ideal, however noble and lofty it be, will ever be able to make shift of the supreme and decisive impulses generated by faith in God and Christ. If the man, who is called to the hard sacrifice of his own ego to the common good, loses the support of the eternal and the divine, that comforting and consoling faith in a God who rewards all good and punishes all evil, then the result of the majority will be, not the acceptance, but the refusal of their duty. The conscientious observation of the ten commandments of God and the precepts of the Church (which are nothing but practical specifications of rules of the Gospels) is for every one an unrivaled school of personal discipline, moral education and formation of character, a school that is exacting, but not to excess. A merciful God, who as Legislator, says - Thou must! - also gives by His grace the power to will and to do. To let forces of moral formation of such efficacy lie fallow, or to exclude them positively from public education, would spell religious under-feeding of a nation. To hand over the moral law to man's subjective opinion, which changes with the times, instead of anchoring it in the holy will of the eternal God and His commandments, is to open wide every door to the forces of destruction. The resulting dereliction of the eternal principles of an objective morality, which educates conscience and ennobles every department and organization of life, is a sin against the destiny of a nation, a sin whose bitter fruit will poison future generations

And in paragraph 43 we find the letter's conclusion:

He who searches the hearts and reins (Psalm vii. 10) is Our witness that We have no greater desire than to see in Germany the restoration of a true peace between Church and State. But if, without any fault of Ours, this peace is not to come, then the Church of God will defend her rights and her freedom in the name of the Almighty whose arm has not shortened. Trusting in Him, "We cease not to pray and to beg" (Col. i. 9) for you, children of the Church, that the days of tribulation may end and that you may be found faithful in the day of judgment; for the persecutors and oppressors, that the Father of light and mercy may enlighten them as He enlightened Saul on the road of Damascus. With this prayer in Our heart and on Our lips We grant to you, as a pledge of Divine help, as a support in your difficult resolutions, as a comfort in the struggle, as a consolation in all trials, to You, Bishops and Pastors of the Faithful, priests, Religious, lay apostles of Catholic Action, to all your diocesans, and specially to the sick and the prisoners, in paternal love, Our Apostolic Benediction.

Now, it should be noted that these critiques of fascism--however strongly worded--are not as black and white as those found regarding communism in Divini Redemptoris. This encyclical was issued a mere five days after the previously discussed Mit Brennender Sorge, and instead of offering critiques of the flaws of fascism it has even harsher statement regarding all communist regimes. This is evident even from paragraph 3:

This all too imminent danger, Venerable Brethren, as you have already surmised, is bolshevistic and atheistic Communism, which aims at upsetting the social order and at undermining the very foundations of Christian civilization

Now, while Pius XI basically says that Catholicism and communism are incompatible while fascism is flawed, we should remember that these documents were issued in 1937--a good deal of time before the outbreak of WWII. Also, Mit Brennender Sorge was suppressed in Germany, Italy, and Nationalist Spain while Divini Redemptoris was given wide publication and distribution--a telling reaction by the regimes of those countries to the Pope's words.

Pius XI died in 1939, before WWII began. His successor Pius XII held much of the same opinions as Pius XI, but had an entirely different set of circumstances with which to work. In this earlier answer I detail some of the criticisms of Pius XII's papacy, as well as some of the responses to those criticisms.

As always, followup questions are encouraged.