Since version 0.7.505, FAF associates ".fafreplay" files with itself, meaning you should be able to double-click and view them. It will download the right featured mod and map required. Later, it will also up/downgrade FAF to past versions (this is planned to be final by FAF milestone 0.8.x)
I attached one as an example (unfortunately, I had to zip it - we'll enable .fafreplay as a legal extension for forum attachments soon).
Tell me if you find any issues with the feature.