It depends what you mean by "study for fun".
I would like to think that many researchers will find what they do professionally as "fun", and so do not feel the urgent need to do something not in their field of specialization.
The most famous of all examples are the contributions to physics from a patent clerk named Albert Einstein; he did have formal training in physics but was not a faculty at that time, and so presumably was still studying physics "for fun".
One of the early breakthrough results of quantum information theory is the famous BB85 protocol for quantum cryptography, by Charles Bennett and Gilles Brassard; neither are physicists by training, although Bennett worked at IBM at the time (and still does) and Brassard specialized (and still does) in cryptography. Both knew physics, and I don't think they brushed up on their physics entirely "for fun", but this example would fit the kind of answer you are looking for.
Depending on your you define "field", you will find many researchers who are accomplished musicians and have studied music extensively, for instance. Although not professionals, some of them are pretty darn good.
In the case of languages, the real barrier is lack of occasion to use "for fun" a language you would have learned. There are plenty of "teach-yourself-German" books, but if you cannot interact in that language in your environment it is unlikely to be much fun.