To answer the question, it is unknown if Fritz and Ymir got married. In the series, it is stated that the royal family has a tradition of marrying close relatives to preserve their bloodline. Historically, Fritz had many wives and concubines, and it is not explicitly stated in the anime or manga if Ymir became one of his wives. However, based on the series’ storyline and the character development of both Fritz and Ymir, it is unlikely that they got married.
Fritz, also known as King Fritz, is depicted as a weak and cowardly leader who abandoned his people and chose to live in luxury behind the walls of Paradis Island. He is also implied to have been manipulated by his advisors, particularly the Tybur family. Meanwhile, Ymir is a tragic character who suffered abuse and discrimination both as a human and a Titan. She was forced to bear the burden of being a Titan shifter for over 60 years, and only found redemption and freedom when she sacrificed herself to save her friends.
Given Fritz’s character and actions, it is doubtful that he would have shown any interest in Ymir aside from her usefulness as a Titan shifter. Moreover, Ymir’s relationship with Fritz was not explored in the series, and her attention and loyalty were directed towards her friends and the cause of Eldia’s restoration. Therefore, it can be concluded that Fritz did not marry Ymir.