In Picard body swap Star Trek TNG fanfiction, trust is a big theme. The crew has to trust that Picard is still Picard, even in a different body. And Picard has to trust his crew to help him through the situation. Another theme is the exploration of different cultures if he swaps with an alien. He gets to experience first - hand what it's like to be part of that alien race, which can lead to new understandings and alliances. There's also the theme of humor, as there are bound to be some funny situations when Picard is in an unexpected body.
One common theme is identity. When Picard swaps bodies, he has to grapple with who he is outside of his own physical form. Another theme is adaptation. He needs to quickly adapt to the new body's abilities and limitations. For example, if he swaps with an engineer, he has to figure out how to use the engineer's technical skills.
A prevalent theme is the exploration of relationships. In a body swap scenario in fanfiction, Picard's relationships with his crew are put to the test. He may find that some crew members treat him differently in another body. There's also the theme of self - discovery. Picard might learn things about his own psyche that were hidden when in his own body. For example, he could discover latent fears or desires. Additionally, there's often a theme of chaos on the ship as the crew adjusts to the situation.