What did Jeanne mean when she said Papa had become a man without a country?

In context, we can take Jeanne's declaration literally. In the face of WWII and the bombing of Pearl Harbor, Papa has lost his identity, his home, his pride, and his ability to take care of his family. In adition to losing his home in the United States and being taken prisoner, Papa has also burned his ties to Japan, literally. Knowing that he will be a target of prejudice, he immediately burns all papers that identify him as native Japanese, along with the Japanese flag he brought from his home in Hiroshima in 1908.