As detailed in the post on Chairman Mao, FDR exchanged letters with Pope Pius XII during World War II. I don't have anything to add about the relationship between FDR and Pius XII, but here are some videos that might interest you.
I strongly urge you to visit the FDR presidential library in Hyde Park, New York if you get a chance. He had 4 terms, there is loads of information to sift through and wonderful displays there. Click here to visit their site.