"He does not sunbathe."
Translation:Il ne bronze pas.
prendre le soleil implies that he is a plant ^^. In French, there is no actual verb for sunbathe. We use bronzer for people (which means to get tanned) or prendre le soleil for plants or objects that actually need sun to function.
WordReference lists both definitions, and discussions about what word to use seem to treat them interchangeably, so I'd say go for it.
That to me would translate to he doesn't tan. Sun bathing means basking in the sun, translation should be acceptable