If I were you, I would work on creating a native Julia implementation of the brand new Arrow C data interface https://github.com/apache/arrow/blob/master/docs/source/format/CDataInterface.rst. A small amount of wrapper code could then be created to take a Julia-generated blob of Arrow memory and write a Parquet file using the C++ API.
If instead you want to use the low-level Parquet write API, you can certainly do that. The main files you need to work with are src/parquet/file_writer.h and src/parquet/column_writer.h. I’m not sure how long it would take to learn enough C++ to work with these APIs since everyone is different. If you have experience with C programming in general and its value types (pointers, references, values) then the jump to C++ is easier since mostly you need to learn about how C++ classes work (constructors, destructors, etc.) and some C++11-specific features like
Aside from C++ language features, there might be some initial shock from working with C++ build systems and packaging libraries for installation.
On the bright side, C++ as a language isn’t going anywhere so the investment of time would pay dividends longer-term.