I am not aware of any contradictions between his writings and Catholic teaching.
He proposes that civilization is built upon the murder in which people come together to take all the aggression that they have with one another, and focus it on a scapegoat.
People covet what the other has, envy and hostility of competing for what the other has threatens to tear the community apart; ritualized murder of the scapegoat allows the community to project those envies and hostilities on the unwitting victim, and the group common identity is thereby maintained. The rising competition of man against man is transposed by group cooperation to carry out the ritual murder.
This is the world of Satan, in Girard’s view, the peace of Satan, if you will. It relies on people not knowing what they are doing, and assuming that the scapegoat victim really is guilty.
With Christ rising, the Satanic lies are exposed for all time, for the process becomes revealed for what it is, a projection of one’s own sin upon that of a victim who has nothing to do with the hostility in the first place. Christ’s rising from the dead proves his innocence, and if innocent, then it is the mob who is guilty of murder.
But that leaves a situation where the peace of Satan, temporary though it may be, is no longer believed in, and no longer can be a release mechanism for the built up aggression that come through constant envy of the other. The peace of Christ is to love one another and see the success of the brother whom you serve as your success.
Without that love of Christ, and now with the mechanisms of scapegoating fully exposed, civilization will explode.
There is nothing contrary to Catholicism in Girard’s anthropology. He even believes that a literal bodily resurrection is the only sufficient explanation for how what followed.