I spend a lot of time scouring for decent Catholic movies on Netflix. Some are more obvious because they have a Biblical theme. Some are Christian but are distinctly Protestant (and thus sometimes heretical). Personally I like to find something that is Catholic, but rather than being Biblical based integrates Catholicism into the story. Here are some of the movies on Netflix that I've discovered:
1) Cheaper by the Dozen (1950)-
I actually grew up with this version. It's based on the memoirs of the Gilbreth family. There's no indication that the family was Catholic, but this version of the movie aligns well with Catholic teaching. There is a scene where a lady from Planned Parenthood (yes that one. although at that time they were peddling birth control and not abortion.) comes to visit the family about the mother heading up their Monteclaire Chapter. The joke is that Dr./Mrs. Gilbreth is the mother of 12 children. There's a great dynamic between the parents as well and with the children. There is a 1952 sequel called Belles on their Toes, but Neflix currently doesn't have it. It takes up the Gilbreth family's life after their father dies suddenly.
2) The Perfect Game (2009)-
This film is about the Mexican Little League Team that won the 1957 Little League World Series. Although the film takes liberties with the historical events, it's clear that faith plays a huge part in the story. There's also some ecumenical stuff going on there as well. After the priest has to return back to Mexico, the players refuse to play without a blessing. A Protestant minister steps in to help shepherd the flock as it continues to travel through the United States. If your concerned, there's no indication that Protestant minister has any intention to convert the boys. He's merely there like any chaplain would be for a solider. It's quite touching that he would care so much for a group of very devout Catholics. Some parts may not be suitable for young children as the film also touches on racism and some of the characters drink heavily. I would view the film first to decide how best to bring up the topic of Christianity and racism during that time period with children.
3) My Italian Secret (2015)-
I love a really good documentary. This one is about how different Catholic Italians- from religious to lay- including the cyclist and Tour de France winner Gino Bartali helped hide Jews during WWII. I don't recall seeing anything particularly graphic but given the content you may want to discuss the history of the Holocaust with your children before having them watch the movie.
4) Rudy (1993)-
This is one of my father's favorite movies. It's another based on a true story sports film. This time it tells the story of Daniel "Rudy" Ruettiger and his determination to enter Nortre Dame and play on it's football team. He is helped along the way with the support of friends, family, support staff and students at Nortre Dame, and clergy. It's not a movie for very young children.
5) The Children of An Lac (1980)-
This film is based on the true story of the evacuation of the Vietnamese orphanage, An Lac, before the fall of Saigon. While the dialogue and acting is at times trite, the story itself is very moving. If you look carefully you will see that Catholicism and a pro-life message is at the core of the movie. There are currently 6 million Catholics in Vietnam, which is a small minority. So the fact that the head of the orphanage is portrayed as a Catholic is so beautiful. The movie isn't particularly violent (you see blood-less dead people and soldiers carrying weapons). So I would say it's okay to show to an elementary age child while discussing the downsides of war and the belief in the dignity of all persons. For older children, you may want to include a discussion about the Vietnam War and that Vietnam today remains one of five nations that is communist which places restrictions on religious freedom (similar to those in communist China).