As Hans and Gothel are from different series, they have never met in canon. Even though Rapunzel and Eugenes' cameos in the first Frozen film hints that they may take place in the same canon. Along with a few Disney crossover games having the two cross paths with each other or having them added to the same team, by the player's choice.
Both Gothel and Hans are manipulative, who had gotten the Princesses of their films to trust them through false love that they had Rapunzel and Anna think that they have for them. As Gothel wishes who forever stay young through the magic within Rapunzel's long hair, while Hans seeks to clam Arendelle's throne for himself by using Anna to reach his goal and had planned to get rid of Elsa once they were married. At the beginning of their films, the two didn't appear as the "bad guys" to its other characters, until they eventually showed them their true colors and how both of them are quick-thinkers, cold, heartless and enjoy being the ones who are in control of their selfish plans. Hans later tried to kill both Elsa and Anna, while Gothel had stabbed Eugene who would of died from his wound if it wasn't for the love Rapunzel has for him, just has Anna was able to stop Hans from killing Elsa through the love she has for her older sister. Both of the magic Gothel and Hans came in contact with has a connection to the forces of nature.
Frozen and the Tangled TV series also shows that Hans doesn't have a strong bond with his 12 older brothers, while Gothel never truly loved her biological child. Gothel and Hans have even recruited allies who have a connection with Flynn Rider and the royal sisters of Arendelle, while keeping their true attentions a secret from them by putting on a show that has them "saving" Rapunzel and Elsa from men who wishes them harm because of the magic they hold. When Hans returned to Arendelle Elsa he placed her in the castle's dungeon, just as Gothel had placed Rapunzel in chains once she uncovered the true and choice to defy her.
Gothel and Hans also have green colored eyes and have visited the kingdoms of their films, Corona and Arendelle, with the goal of taking someone from them. The Tangled TV series even has a nightmare version of Gothel being hit in the head by Rapunzel with her frying pan, while in Frozen II Elsa comes across a frozen water memory figure of Hans and destroys it with her powers.
Gothans is a villain ship in the Rise of the Brave Tangled Frozen Dragons crossover fandom. The ship could be due to fans who enjoy Disney crossover ships with villains, and the two films coming out close together. A few fanfics have the two teaming up to make their enemies lives horrible, as well as the two taking a page from each other's books. Gothel is commonly viewed as a witch in fanon, just has Hans is sometimes given power over fire.
On AO3, the ship has 2 fanfics, while fanfiction.net has 3 in its crossover category. Along with it having a small fanbase on Tumblr.
- They both appear in the Once Upon A Time series.
- In Kingdom Hearts III, both Gothel and Hans were turned into a very powerful Heartless who served as the final bosses of their home worlds.