Is the Catholic Church Arminian rather than Calvinist?
The short answer
Neither label fits: the Church came before Arminianism and isn't a product of it. Better to say Calvinism and Arminianism each agree with Catholicism on some points and differ on others.
The Church came first
The Catholic Church cannot be called Arminian; it predates Arminianism and is not a product of it.
Calvinism
John Calvin's system, remembered as TULIP: total depravity, unconditional election, limited atonement, irresistible grace, perseverance of the saints.
Arminianism
Named for Jacobus Arminius, summarized in the five articles of the Remonstrants: apart from grace man can do nothing truly good, conditional election, unlimited atonement, resistible grace, and the possibility of apostasy.
Agreement and disagreement
Catholic theologians from Aquinas to Bellarmine have taught unconditional election, as Calvinists do; but the Church does not teach that all believers are predestined to persevere. With Arminians, the Church teaches universal redemption; but she allows for the possibility of unconditional election.