With the freely downloadable FIT SDK you can process FIT files using Java and C. I convert FIT to GPX that way and create summaries and statistics from FIT files.
You can also convert FIT files to TCX from a couple of websites and from Garmin Connect too.
OK, I might look at the FIT SDK. But, you say I can convert FIT files to TCX using Garmin Connect. How? I don't see any buttons for this, I'm probably not on the correct page.