Your question looks like career advice so might be off-topic here.
I am sometimes working on free software, but I am not an expert on that.
First, most major (or large and significant) free software (Linux kernel, GCC compiler, Firefox browser) are mostly (but not entirely) developed by paid professionals. In other words, the idea that major free software is developed by part-time hobbyists is today mostly a myth (it might be still true for many one-man projects; it is false for multi-million lines of source code free
software). Free software is very serious business.
Then, as a job market, the free software communities are very demanding and extremely competitive (world-wide). You are unlikely (IMHO) to find a paid job if you are not known by some free software meritocracy.
Hence my advice is to start working on your own on some existing free software project you like (you probably could check that your work contract does not legally prohibit that). Once you are known for some positive contributions to some free software things might become different. Contributing to free software (in a regular and transparent manner) require both technical skills (understanding the code base) and social skills (interacting with the community).
BTW, things are different if your are employed by some corporation, or if you are self-employed. Several free-lancers are able to sell some part-time contributions to free software. Several corporations permit some workers to work on some free software part-time.
So you could start today by finding some interesting (for you!) free software, e.g. on github, then contributing some code to it.